A model predictive control method based on dynamic output feedback strategy

Abstract

The present invention discloses a model predictive control method based on a dynamic output feedback strategy, which is applied to polyhedral uncertain systems. When physical devices in the polyhedral uncertain system are operating, data is transmitted through sensors. The model predictive control process is as follows: a dynamic output feedback strategy including a controller and an observer is established. Based on the model predictive control problem, the polyhedral uncertain system, the controller, and the observer are described using state equations. The observer is used to constrain the data transmitted by the sensor and process measurement wild values in the data. The controller is used to perform model predictive control on the processed output data to obtain the control input at the next moment, and the control input is applied to the physical device through an actuator. The present invention is targeted at polyhedral uncertain systems with measurement wild values. The study uses a saturation function to study an observer-based dynamic output feedback strategy, mitigate the impact of measurement wild values, and ensure the robustness and asymptotic stability of the system.

Description

Technical Field

[0001] The present invention belongs to the technical field of control engineering, and in particular relates to a model predictive control method based on a dynamic output feedback strategy. Background Art

[0002] Over the past few decades, pattern predictive control (MPC) has garnered significant attention from both academic and engineering communities. At each instant, an online optimization problem is solved based on current measurements to compute a series of control actions within a predicted future horizon, but only the first one is actually implemented on the device. At the next instant, the optimization problem must be reformulated based on new measurements, and the control inputs determined by this problem are applied to the polyhedral uncertain system.

[0003] For example, Chinese patent publication CN110780649A discloses a novel hybrid constrained model predictive tracking control optimization design method for industrial processes, which belongs to the field of advanced industrial process control and includes the following steps: Step 1: Establishing a novel polyhedral discrete switching system model for industrial processes; Step 2: Minimum-maximum optimization design of model predictive tracking control. This design method transforms the multi-stage industrial process input-output model into a polyhedral switching system model. This model is a new representation of the original system under the "worst" condition. For such a model, it is converted into an extended new state space model consisting of system state error and output tracking error. Under this model, a fault-tolerant predictive controller based on the switching mode is designed. This controller is the minimum control input that overcomes the maximum interference and minimizes the upper bound of the performance indicator, achieving the goals of high-precision control and energy saving to a certain extent.

[0004] To handle the inevitable parameter uncertainties in modeling, the so-called Robust Multi-Procedure Processing (RMPC) method was developed. However, in practical engineering, the states of polyhedral uncertain systems are not always fully accessible, which means that RMPC strategies may be ineffective. Therefore, a new RMPC strategy based on output feedback control is proposed to address the unmeasurable states of polyhedral uncertain systems.

[0005] It's worth noting that the conditions achieved using static output feedback-based RMPC strategies are somewhat conservative, as the output matrix typically requires full row sorting, or the input matrix requires full column sorting. To overcome this obstacle, dynamic output feedback RMPC (OFRMPC) has emerged. However, in the real world, the states of polyhedral uncertain systems are often unmeasurable state variables. Therefore, observer-based output feedback MPC strategies are an indispensable and effective approach to address this problem.

[0006] Polyhedral uncertainty systems are subject to various factors, and measurement outliers are an inevitable problem. These can degrade the estimation performance of these systems, thereby affecting their stability. Therefore, addressing measurement outliers in these systems, improving their state prediction performance, and ultimately making them more stable, is an important topic. Summary of the Invention

[0007] The present invention provides a model predictive control method based on a dynamic output feedback strategy. For a polyhedral uncertain system with measurement outliers, the design of an observer-based dynamic output feedback strategy is studied using a saturation function to alleviate the impact that may be brought about by measurement outliers, thereby ensuring the robustness and asymptotic stability of the system.

[0008] A model predictive control method based on a dynamic output feedback strategy is applied to polyhedral uncertain systems. When the physical devices in the polyhedral uncertain system are operating, data is transmitted through sensors. The model predictive control process is as follows:

[0009] A dynamic output feedback strategy including a controller and an observer is established. Based on the problem of model predictive control, the polyhedral uncertain system, the controller and the observer are described by the state equations respectively.

[0010] The observer with dynamic output feedback strategy is used to constrain the data from the sensor and process the outliers in the data.

[0011] The controller is used to perform model predictive control on the processed output data to obtain the control input at the next moment and act on the physical device through the actuator.

[0012] Furthermore, the polyhedral uncertain system is described by the state equation as follows:

[0013]

[0014] Where x(k), u(k), and y(k) represent the state, control input, and measured output, respectively, and k represents the current sampling time. A(k), B(k), and C(k) are unknown matrices of appropriate dimensions that belong to the following convex hull:

[0015]

[0016] Where, θ∶=(A(k),B(k),C(k)), are the vertices of the convex hull Δ, which is used to describe the uncertainty of a polyhedral uncertain system.

[0017] The observer is described by the state equation as follows:

[0018]

[0019] in, is the state estimate, is the output estimate, H(k) is the parameter matrix to be designed, and A (0) ,B (0) ,C (0) is the polyhedral uncertain system matrix, Sat σ(k) (r(k)) is the saturation function, defined as follows:

[0020]

[0021] in, r (l) (k) represents the lth input of the vector r(k); in each step, the saturation level σ(k) is time-varying and is adaptively determined by the following difference equation:

[0022] σ(k+1)=ασ(k)+(r(k)) T ι(k)(r(k))

[0023] Where α∈[0,1), ι(k) is a predetermined positive definite matrix.

[0024] The controller is described by the state equation as follows:

[0025]

[0026] Among them, u(k+n|k) and is the n-step prediction of the control input and state estimation at time k, and F(k+n|k) is the feedback gain designed through optimization. According to the requirements of actual engineering, the constraints on the control input and state are as follows:

[0027]

[0028] in, and is a known scalar.

[0029] The polyhedral uncertain system is further described as follows:

[0030] Defining the estimation error The closed-loop polyhedral uncertain system within the prediction range is expressed in the following form:

[0031]

[0032] ζ(k)=[1 e T(k)] T

[0033] The following expanded polyhedral uncertain system is obtained:

[0034]

[0035] in,

[0036]

[0037]

[0038] The controller is further described by the min-max cost function:

[0039] min F(k),H(k) max (A(k),B(k),C(k))∈Δ J ∞ (k),

[0040] Among them, F(k), H(k) are the parameter matrices to be designed, A(k), B(k), C(k) are the parameter matrices of the system, and the objective function J ∞ (k) is defined as:

[0041]

[0042] Where ζ(k)=[1e T (k)] T , To estimate the error, Q1, Q2, Q3, Q4, Q5, R represents a symmetric and positive definite weighting matrix, Q = diag{Q1, Q2, Q3, Q4, Q5}.

[0043] According to the minimum-maximum cost function, the following online optimization problem Op1 is determined to solve the required parameter matrices F(k) and H(k):

[0044] Op1:min F(k),H(k) max (A(k),B(k),C(k))∈Δ J ∞ (k),

[0045]

[0046]

[0047] ζ(k+n|k)∈Γ(P(k+n|k),5ρ), n=0,1,2,...

[0048] where Γ is the so-called terminal constraint set, defined as:

[0049]

[0050] Wherein, P(k+n|k) represents the positive definite matrix of the quadratic function.

[0051] The polyhedral uncertain system includes two conditions: hard constraints or no hard constraints;

[0052] For the condition without hard constraints, when designing the controller, we first give a sufficient condition to satisfy the terminal constraint set conditions in Op1, namely ζ(k+n|k)∈Γ(P(k+n|k),5ρ); then, we propose an auxiliary optimization problem to find the suboptimal solution of the unconstrained system; by solving the line-assisted optimization problem, we obtain a sufficient condition to ensure the stability of the closed-loop polyhedral uncertain system.

[0053] The auxiliary optimization problem is solved by using inequality analysis technology and Lyapunov stability theory to obtain F(k), H(k), so as to ensure the stability of the polyhedral uncertain system while processing measurement outliers.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] Due to the existence of measurement outliers, for polyhedral uncertain systems, this paper introduces an observer with a saturation function to deal with the dynamic OFRMPC problem; the upper bound of the quadratic cost function is derived for the optimization problem Op4; and an online dynamic OFRMPC algorithm is proposed to obtain some controllers to make the closed-loop constrained polyhedral uncertain system asymptotically stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a structural diagram of a polyhedron uncertain system in the model predictive control method of the present invention;

[0057] Figure 2 This is a trend diagram of estimation errors at different saturation levels in an embodiment of the present invention;

[0058] Figure 3 1 is a state response effect diagram of an open-loop and closed-loop polyhedron uncertain system in an embodiment of the present invention. DETAILED DESCRIPTION

[0059] The present invention will be described in further detail below with reference to the accompanying drawings and embodiments. It should be noted that the embodiments described below are intended to facilitate understanding of the present invention and do not have any limiting effect on the present invention.

[0060] like Figure 1 As shown in Figure 1, a model predictive control method based on a dynamic output feedback strategy is applied to a polyhedral uncertain system. When the physical devices in the polyhedral uncertain system are running, data is transmitted through sensors. The model predictive control process is as follows:

[0061] A dynamic output feedback strategy consisting of a controller and an observer is established. Based on the problem of model predictive control, the polyhedral uncertain system, the controller and the observer are described by state equations respectively.

[0062] The observer of the dynamic output feedback model is used to constrain the data sent by the sensor and process the measurement outliers in the data;

[0063] The controller is used to perform model predictive control on the processed output data to obtain the control input at the next moment and act on the physical device through the actuator.

[0064] For a polyhedral uncertain system subject to measurement outlier constraints, a model predictive control problem based on a dynamic output feedback strategy is established, which includes the following steps:

[0065] Firstly, for the problem to be solved, the state equation is used to describe the polyhedral uncertain system, observer and controller.

[0066] 1) Consider the following polyhedral uncertain system:

[0067]

[0068] Where x(k), u(k), and y(k) represent the state, control input, and measured output, respectively, and k represents the current sampling time. A(k), B(k), and C(k) are unknown matrices of appropriate dimensions that belong to the following convex hull:

[0069]

[0070] Where, θ∶=(A(k),B(k),C(k)), are the vertices of the convex hull Δ, which is used to describe the uncertainty of the system.

[0071] 2) Marking The controller for the observer-based polyhedral uncertain system is designed as follows:

[0072] 3)

[0073] in, is the state estimate, is the output estimate, H(k) is the parameter matrix to be designed, and A (0) ,B (0) ,C (0) is the polyhedral uncertainty system matrix, and the saturation function is defined as follows:

[0074]

[0075] in, r (l) (k) represents the lth input of the vector r(k). In each step, the saturation level σ(k) is time-varying and is adaptively determined by the following difference equation:

[0076] σ(k+1)=ασ(k)+(r(k)) T ι(k)(r(k)) (4)

[0077] where α∈[0,1), ι(k) is a predetermined positive definite matrix.

[0078] In the observer-based polyhedral uncertain system, a specially designed saturation function is adopted to mitigate the impact of possible measurement outliers, which limit the innovation fed back to the observer (i.e., the difference between the measured and estimated outputs). Specifically, it can be seen from (4) that when the innovation at time step k becomes smaller (i.e., the estimation error becomes smaller), the saturation level σ(k+1) will become lower, which means that the corresponding constraint imposed on the innovation at time step k+1 will be stricter.

[0079] For simplicity, we define There exists a diagonal matrix And the following inequality is satisfied:

[0080]

[0081] in,

[0082] 4) For the polyhedral uncertain system (3), the following controller is considered under the model predictive control framework:

[0083]

[0084] Among them, u(k+n|k) and is the n-step prediction of the control input and state at time k, and F(k+n|k) is the feedback gain designed through optimization. Based on the actual requirements of the actual project, the constraints on the control input and state are as follows:

[0085]

[0086] in, and is a known scalar.

[0087] Defining the estimation error The closed-loop polyhedral uncertain system within the prediction range can be expressed in the following form:

[0088]

[0089] ζ(k)=[1 e T (k)] T

[0090] We can obtain the following expanded polyhedral uncertain system:

[0091]

[0092] in,

[0093]

[0094]

[0095]

[0096] It can be found that the polyhedral uncertain system corresponding to formula (9) is polyhedral uncertain. In addition, for the above augmented closed-loop polyhedral uncertain system, we consider the following form of minimum-maximum cost function to design the controller:

[0097] min F(k),H(k) max (A(k),B(k),C(k))∈Δ J ∞ (k) (11)

[0098] The objective function J ∞ (k) is defined as:

[0099]

[0100] Q1, Q2, Q3, Q4, Q5, R denote symmetric and positive definite weight matrices, Q = diag{Q1, Q2, Q3, Q4, Q5}. Based on the min-max problem in Equation (11), the following online optimization problem is proposed to design the controller under the output feedback MPC framework:

[0101] Op1:min F(k),H(k) max (A(k),B(k),C(k))∈Δ J ∞ (k),

[0102]

[0103]

[0104] ζ(k+n|k)∈Γ(P(k+n|k),5ρ), n=0,1,2,...

[0105] where Γ is the so-called terminal constraint set, defined as:

[0106]

[0107] where P(k+n|k) represents the positive definite matrix of the quadratic function. It should be noted that only the first component of a set of prediction inputs {u(k), u(k+1|k), u(k+2|k), ...} will actually be applied to the device at each moment. More specifically, an auxiliary optimization problem Op1 is given to solve the required parameter matrices F(k), H(k) under which the stability of the closed-loop polyhedral uncertain system is guaranteed. To achieve this goal, for the parameter k, the following two requirements need to be met simultaneously: an auxiliary optimization problem is provided to represent the problem Op1 so that a suboptimal solution can be obtained; and according to the obtained parameter matrices F(k), H(k), the closed-loop observer-based polyhedral uncertain system (3) with saturation function is asymptotically stable.

[0108] For polyhedral uncertain systems with or without hard constraints, we obtain some sufficient conditions to ensure the stability of the proposed polyhedral uncertain system and derive the corresponding model predictive control algorithm with dynamic output feedback strategy. The specific steps are as follows:

[0109] 1) Observer-Based Unconstrained MPC Controller Design: We propose sufficient conditions for constrained polyhedral uncertain systems to guarantee the desired performance through a quadratic function approach. Based on these conditions, we derive a dynamic output feedback controller within the RMPC framework. Specifically, we first provide sufficient conditions for satisfying the terminal constraint set in Op1, namely, ζ(k+n|k)∈Γ(P(k+n|k),5ρ). We then propose an auxiliary optimization problem to find a suboptimal solution for the unconstrained system. Furthermore, we utilize inequality analysis techniques to address the unavailable state x(k) in the auxiliary problem and provide a solution to this problem with another auxiliary problem. Finally, by solving this online auxiliary optimization problem, we derive sufficient conditions for the stability of the closed-loop polyhedral uncertain system.

[0110] Definition 1: If η(k)∈Γ implies η(k+1)∈Γ, then for the system (1) under the control law (6), the set Γ is robust positive invariant (RPI).

[0111] For the online optimization problem Op1, the following two conditions need to be met. Then, for Op1, Γ(P(k+n|k),5ρ) is the terminal constraint set:

[0112] C1: There exists a quadratic function

[0113]

[0114] satisfy

[0115] V(ζ(k+n+1|k))-V(ζ(k+n|k)) ≤-ζ T (k+n|k)Qζ(k+n|k)-u T (k+n|k)Ru(k+n|k)(15)

[0116] C2: The set Γ(P(k+n|k),5ρ) is a robust positive invariant set.

[0117] Next, we will discuss the above two conditions one by one. First, according to the RLMI method, the following theorem gives a sufficient condition for the polyhedral uncertain system (9).

[0118] Theorem 1: Let γ>0, Given {F(k),H(k)} 0≤k≤N , if there exists a series {P(k)} 0≤k≤N+1 and and many positive scalars {τ(k)} 0≤k≤N and the real scalar {ε(k)} 0≤k≤N ,So

[0119]

[0120] in

[0121]

[0122]

[0123]

[0124]

[0125]

[0126] 2) Auxiliary optimization issues

[0127] For unconstrained systems, we will discuss how to deal with OP1. OP1 is an optimization problem with infinite time horizon and parameter uncertainty, which is difficult to handle directly. Instead, an auxiliary optimization problem is proposed to find a suboptimal solution.

[0128] Obviously, if condition (19) holds, then we have equation (14). This means that ζ(∞|k) = 0 and V(∞) = 0. Adding both sides of equation (16) from n = 0 to n = ∞ and using equation (11) we get

[0129] J ∞ (k)≤V(k)=ζ T (k)P(k)ζ(k)≤5ρ (27)

[0130] This formula shows

[0131] max (A(k),B(k),C(k))∈Δ J ∞ (k)≤5ρ (28)

[0132] This gives the upper bound of the objective function of OP1. Based on the above analysis, we are ready to propose the following auxiliary optimization problem for the unconstrained polyhedral uncertain system:

[0133]

[0134] Since the state x(k) cannot be measured, condition (25) cannot be checked online. Next, we will deal with the problem of unavailable states in the constraint equation (25). Before proceeding, the following are important assumptions.

[0135] Assumption 1. Based on the initial state of the polyhedral uncertain system (1), the known set is as follows:

[0136] x(0)∈{x(k)|x T (k)S -1 x(k)≤1} (29)

[0137] Among them, S is a matrix set in advance through experience.

[0138] Lemma 3: Consider the polyhedral uncertain system (1) governed by equation (6), if there exists a symmetric positive definite matrix Given Assumption 1, the following holds

[0139]

[0140]

[0141]

[0142]

[0143] in, mark vertices, l = 1, 2, ..., L, then the condition (25) can be always ensured.

[0144] According to Assumption 1 and Lemma 3, we can transform the problem Op2 into the following approximate optimization on solvability:

[0145]

[0146] 3) Feasibility and stability.

[0147] Next, we will clarify the feasibility of the proposed problem. To take a step forward, we will show the stability of the polyhedral uncertain system (1) governed by Equation (6).

[0148] Theorem 2. Given a symmetric positive definite matrix Q i (i = 1, ..., 5) and R, and we consider the polyhedral uncertain system (1) controlled by Equation (6). If a feasible solution to the optimization problem Op3 exists at the initial time k, then a corresponding feasible solution also exists at any future time t>k. Moreover, the closed-loop polyhedral uncertain system is asymptotically stable, and Equation (6) determines the feedback gain.

[0149] 4) Observer-based hard-constrained MPC controller design

[0150] Based on the previous work, we will discuss the MPC problem for polyhedral systems with hard constraints and obtain some sufficient conditions. Finally, under certain conditions, we propose an algorithm for solving online optimization problems.

[0151] Controller Design with Saturation Function: First, several inequalities are proposed to ensure hard constraints on input and state in Equation (7). Then, a controller is designed based on the optimization problem and the corresponding algorithm is proposed under the MPC framework for constrained polyhedral uncertain systems.

[0152] Lemma 4: If there exists a symmetric positive definite matrix and matrix ω, so that the input and state hard constraints in (7) are satisfied, then the following conditions hold:

[0153]

[0154]

[0155] For the constrained polyhedral uncertain system, according to Lemma 4, the further auxiliary optimization problem can be obtained as follows:

[0156]

[0157] Based on the above discussion, we give the following theorem that the polyhedral uncertain system (1) with hard constraints governed by Eq. (6) is asymptotically stable.

[0158] Theorem 3: Equations (1) and (7) are governed by Equation (6), and we consider a polyhedral uncertain system with hard constraints. At the initial time k, if the optimization problem Op4 is feasible, then for all future times t>k, the optimization problem Op4 is also feasible. In addition, the closed-loop polyhedral uncertain system is stable, and the feedback gain

[0159] 5) RMPC algorithm for constrained polyhedral uncertain systems

[0160] Considering the dynamics of the RMPC strategy, an observer-based algorithm for constrained polyhedral uncertain systems with a saturation function is given:

[0161] Offline part:

[0162] Select initial state and an appropriate matrix S such that x(0)∈{x(k)|x T (k)S -1 x(k)≤1} is feasible when k=0.

[0163] Online section:

[0164] Step 1. At time k, solve the optimization problem Op4 and obtain the controller gains F(k) and H(k) based on the parameters of the offline part through the observer.

[0165] Step 2. Calculation And will Implement it into the system and then return to Step 1.

[0166] To verify the effect of the present invention, an industrial distillation process is taken as an example to construct a polyhedron uncertain system and verify the effectiveness of the proposed model predictive control strategy.

[0167] An industrial distillation process has two manipulated variables, reflux and boiling ratio, and two controlled variables, top and bottom composition. By selecting the same sampling period, a discrete-time polyhedral uncertainty system is obtained. From a practical perspective, parameter uncertainties are factored into the system matrix of the polyhedral uncertainty system. Consider the following polyhedral uncertainty system model:

[0168]

[0169]

[0170] The corresponding initial value

[0171] Then, in order to better meet the polyhedron uncertainty requirements of the actual polyhedron uncertain system, the parameters of the polyhedron uncertain system are selected as follows:

[0172]

[0173]

[0174]

[0175]

[0176] The upper limits of input and state are respectively given by and Given, the weight matrix is chosen as

[0177] The simulation results are as follows Figure 2 and Figure 3 As shown. To be precise, Figure 2 As shown in Figure 2, the estimation error e(k) trends of the polyhedron uncertainty system with a fixed saturation level and the polyhedron uncertainty system with an adaptive saturation level are described. It is not difficult to see that the proposed algorithm for adaptively changing the saturation level can effectively reduce the influence of measurement outliers, thereby improving the estimation performance. Figure 3 As shown in Figure 3, the state trends of the polyhedral uncertain system without and with a controller are described. Moreover, under the proposed dynamic OFRMPC algorithm, the closed-loop polyhedral uncertain system is more stable than the open-loop polyhedral uncertain system.

[0178] The embodiments described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A model predictive control method based on dynamic output feedback strategy, characterized in that: Applied to polyhedral uncertain systems, when the physical devices in the polyhedral uncertain system are running, data is transmitted through sensors; the model predictive control process is as follows: A dynamic output feedback model predictive control strategy including a controller and an observer is established. Based on the problem of model predictive control, the polyhedral uncertain system, controller and observer are described respectively by state equations. The polyhedral uncertain system is described by the state equation as follows: Where x(k), u(k), and y(k) represent the state, control input, and measured output, respectively, and k represents the current sampling time. A(k), B(k), and C(k) are unknown matrices of appropriate dimensions that belong to the following convex hull: in, l = 1, 2, ..., L are the vertices of the convex hull Δ, which is used to describe the uncertainty of the polyhedral uncertain system; The observer is described by the state equation as follows: in, is the state estimate, is the output estimate, H(k) is the parameter matrix to be designed, and A (0) ,B (0) ,C (0) is the polyhedral uncertain system matrix, Sat σ(k) (r(k)) is the saturation function, defined as follows: in, r (l) (k) represents the lth input of the vector r(k); in each step, the saturation level σ(k) is time-varying and is adaptively determined by the following difference equation: σ(k+1)=ασ(k)+(r(k)) T i(k)(r(k)) Where, α∈[0,1), ι(k) is a predetermined positive definite matrix; The observer with dynamic output feedback strategy is used to constrain the data from the sensor and process the outliers in the data. The controller is used to perform model predictive control on the processed output data to obtain the control input at the next moment and act on the physical device through the actuator.

2. The model predictive control method based on dynamic output feedback strategy according to claim 1, characterized in that: The controller is described by the state equation as follows: Among them, u(k+n|k) and is the n-step prediction of the control input and state estimation at time k, and F(k+n|k) is the feedback gain designed through optimization. According to the requirements of actual engineering, the constraints on the control input and state are as follows: in, and is a known scalar.

3. The model predictive control method based on dynamic output feedback strategy according to claim 2, characterized in that: The polyhedral uncertain system is further described as follows: Defining the estimation error The closed-loop polyhedral uncertain system within the prediction range is expressed in the following form: The following expanded polyhedral uncertain system is obtained: in, 4. The model predictive control method based on dynamic output feedback strategy according to claim 3 is characterized in that: The controller is further described by the min-max cost function: Among them, F(k), H(k) are the parameter matrices to be designed, A(k), B(k), C(k) are the parameter matrices of the system, and the objective function J ∞ (k) is defined as: Where ζ(k)=[1e T (k)] T , is the estimation error, Q1, Q2, Q3, Q4, Q5, R represent symmetric and positive definite weight matrices, Q = diag{Q1, Q2, Q3, Q4, Q5}.

5. The model predictive control method based on dynamic output feedback strategy according to claim 4 is characterized in that: According to the minimum-maximum cost function, the following online optimization problem Op1 is determined to solve the required parameter matrices F(k) and H(k): ζ(k+n|k)∈Γ(P(k+n|k),5ρ),n=0,1,2,... where Γ is the so-called terminal constraint set, defined as: Wherein, P(k+n|k) represents the positive definite matrix of the quadratic function.

6. The model predictive control method based on dynamic output feedback strategy according to claim 5, characterized in that: The polyhedral uncertain system includes two conditions: hard constraints or no hard constraints; For the condition without hard constraints, when designing the controller, we first give a sufficient condition to satisfy the terminal constraint set conditions in Op1, namely ζ(k+n|k)∈Γ(P(k+n|k),5ρ); then, we propose an auxiliary optimization problem to find the suboptimal solution of the unconstrained system; by solving the line-assisted optimization problem, we obtain a sufficient condition to ensure the stability of the closed-loop polyhedral uncertain system.

7. The model predictive control method based on dynamic output feedback strategy according to claim 6, characterized in that: The auxiliary optimization problem is solved by using inequality analysis technology and Lyapunov stability theory to obtain F(k), H(k), so as to ensure the stability of the polyhedral uncertain system while processing measurement outliers.

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