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State constrained control method for nonlinear system
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A nonlinear system, state-constrained technology, applied in the field of control, can solve the problem of not being able to provide
Inactive Publication Date: 2013-12-18
HARBIN INST OF TECH
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[0008] The present invention is to solve the problem that the existing controller needs manual intervention and cannot provide any success guarantee, the non-linear system makes the traditional method difficult to apply and the optimization algorithm has low efficiency in the non-linear system, and provides a A Controller Design Method for State Constrained Systems of Nonlinear Systems
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specific Embodiment approach 1
[0018] Specific Embodiment 1: A method for designing a state-constrained controller for a nonlinear system in this embodiment is implemented in the following steps:
[0019] Step 1, establishing a mathematical model of a nonlinear strict feedback system;
[0020] Step 2. Deriving a backstepping recursive controller with full state constraints;
[0021] Step 3: Verify the feasibility condition detection of the full state constraints.
[0022] The effect of this implementation mode:
[0023] In this embodiment, bounded Lyapunov functions are used to discuss the synthesis of controllers for systems with nonlinear constraints. When used in this context, this embodiment defines their name as the bounded Lyapunov function, which is characterized in that when the parameters of the function are close to a certain limit value, the value of the function will tend to infinity. The key issue concerned in this embodiment is to ensure the boundedness of the bounded Lyapunov function of t...
specific Embodiment approach 2
[0025] Specific implementation mode two: the difference between this implementation mode and specific implementation mode one is: the mathematical model of establishing a nonlinear strict feedback system described in step one is specifically:
[0026] Consider the following strict feedback nonlinear system of the form:
[0027] x · i = f i ( x ‾ i ) + g i ( x ‾ i ) x i + 1 , i = 1,2 , . . . , n - 1 - ...
specific Embodiment approach 3
[0034] Embodiment 3: The difference between this embodiment and Embodiment 1 or 2 is that the design of the full-state constrained backstepping recursive controller described in step 2 includes the following four parts:
[0035] Before the design of the controller, give the following lemmas that will be used:
[0036] Lemma 1: (Existence and uniqueness theorem of solutions) for the initial value problem
[0037] ξ · = h ( t , ξ ( t ) ) , ξ ( σ 0 ) = e 0 , - - - ( 2 )
[0038] in suppose in is an open set, is an interval that satisfies the following assu...
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Abstract
The invention relates to a control method, in particular to a state constrained control method for a nonlinear system. The method mainly solves the problems that an exiting controller needs manual intervention and can not provide any success guarantee, the nonlinear system brings difficulty to the application of a traditional method, and the efficiency of optimization algorithms of the nonlinear system is low. The method includes the following steps: step1, establishing a mathematical model of a nonlinear strict-feedback system, step2, designing a total-state constraint contragradience recursion controller, and step3, detecting total-state constraint feasible conditions. The method is applied to the automatic control field.
Description
technical field [0001] The invention relates to a control method, in particular to a control method of a state-constrained system of a nonlinear system. Background technique [0002] Constraints are ubiquitous in physical systems and can take the form of halts, saturation, and performance and safety specifications. Violation of constraint conditions during system operation may lead to system performance degradation, and in severe cases will endanger or damage the system. Due to practical requirements and theoretical challenges, controller design for constrained systems has become a hot topic in recent decades. [0003] Inspired by the above problems, the present invention tries to design a controller by using bounded Lyapunov function (BLF) method for nonlinear systems with strict feedback form. Unlike the conventional globally positive definite and radially unbounded Lyapunov function (QLF), BLF tends to infinity when its parameters approach certain bounds. Violation of ...
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