Energy allocation method for maximizing the utility of a monotonically increasing convex function system under random energy arrival conditions

Abstract

This invention investigates the offline one-dimensional resource allocation problem of maximizing the utility of a convex increasing function system within a given time frame, under both energy causality (hard) and energy saturation (soft) constraints. Utilizing the Karush-Kuhn-Tucher condition, a modified tunneling strategy based on geometric programming is proposed, considering only causal hard constraints and saturation soft constraints. A computational method for allocating energy to various time slots is presented. This method is particularly advantageous when the geometric allocation line simultaneously encounters either the upper or lower edge of the energy constraint. This invention solves the energy allocation problem of maximizing the utility of an increasing convex function system under causal hard constraints and saturation soft constraints.

Description

Technical Field

[0001] This invention relates to an algorithm for resource allocation in energy harvesting systems. This algorithm can maximize the system utility of a monotonically increasing convex utility function under conditions of random energy arrival, achieving one-dimensional optimal energy allocation. Background Technology

[0002] In recent years, energy harvesting systems have received widespread attention in fields such as communication systems, wearable or implantable devices, structural health monitoring systems, wireless sensor networks, and vehicle area networks. For example, EH devices can serve as Road Side Units (RSUs) in vehicle edge computing networks, performing tasks such as vehicle safety warnings, vehicle dispatching, vehicle control, and human information services. In other application examples, in fog computing scenarios, EH devices can act as human servers or fog nodes, collecting, storing, processing data, and forwarding it to the network edge (IoT gateway). Energy harvesting systems can perform various tasks, including specific functions such as sensing, transmitting, diagnosing, treating, and preventing diseases; industrial process machine monitoring and control; vehicle safety warnings, monitoring, and control; information services; and intelligent transportation. The harvested energy can be used to replenish the batteries of IoT nodes, and can come from natural resources (such as solar energy) and artificial resources. Therefore, studying the distribution of energy across time slots under conditions of random energy arrival and causal flow between time slots is of great significance for improving system performance, maximizing energy utilization, and achieving maximum system utility.

[0003] Previous literature proposed the tunnel policy method [1]. When the energy distribution line can encounter multiple upper and lower edges, the tunnel policy may obtain a non-optimal distribution solution. Literature [2] pointed out the optimal solution structure, but did not give the specific solution method and steps.

[0004] [1]K.Tutuncuoglu and A.Yener,

[0005] "Optimum transmission policies for battery limited energy harve stingnodes," IEEE Transactions on Wireless Communications, vol.11, no.3, pp.1180-1189, March 2012.

[0006] [2] O. Ozel, K. Tutuncuoglu, J. Yang, S. Ulukus, and A. Yener, “Transmission with energy harvesting nodes in fading wireless channels:

[0007] Optimal policies,” IEEE Journal on Selected Areas in Communica tions, vol.29, no.8, pp.1732-1743, Sep.2011 Summary of the Invention

[0008] The technical problem solved by this invention is: based on existing strategies, a method for optimizing energy allocation in energy harvesting systems using the KKT method is proposed, which can achieve greater system utility than the tunneling strategy;

[0009] The technical solution of this invention is characterized by including the following steps:

[0010] 1) First, an energy harvesting model is proposed, and two constraints on the energy harvesting problem are given: causal hard constraint and saturation soft constraint. The objective function is defined, and the value is maximized in the end.

[0011] 3) Since the objective function of the problem to be optimized is a convex function and simultaneously follows both causal hard constraints and saturation soft constraints, this problem is an optimization problem following stochastic energy arrival. Based on the tunneling strategy, the relevant parameters are defined, and it is pointed out that the proposed solution has a better solution than the tunneling strategy. The objective function is analyzed using KKT optimization conditions, and the corresponding Lagrangian function is given in combination with the constraints. The Lagrangian multiplier for the causal hard constraint is u, and the Lagrangian multiplier for the saturation soft constraint is λ.

[0012] The following algorithm is given to solve the problem;

[0013] The one-dimensional assignment algorithm (EEBP - Effective Boundary Touch Strategy) under causal hard constraints and saturated soft constraints is characterized by the following steps:

[0014] 1) When l ueff =max{l u1 , l u2 ,..,l ueff}, l=l u1 ,l u2 ,…,l ueff It is the set of time slots where p1 touches the upper bound of the longest available channel. The last time slot is taken as the valid upper bound, and then... That is, under the saturation soft constraint condition, all multipliers before s1 are 0; collect data from time slot 1 to time slot s = l. ueff The slope p1 = p0[l ueff The energy of ], where n1 = l ueff ;

[0015] 2) Otherwise, l λeff =max{l λ1 ,l λ2 ,…,l λeff}, l=l λ1 , l λ2 , ..., l λeff l = l λ1 ,l λ2 , ..., l λeff It is the set of time slots where p1 touches the lower bound of the longest available channel. The last time slot is taken as the valid lower bound touch, and then... The multipliers are all 0 under the hard constraint of causality, meaning that all multipliers before s1 are 0; collect data from time slot 1 to time slot l = l. λeff The slope p1 = p max [l λeff The energy of ], n1 = l λeff ;

[0016] 3) Use the modified and updated parameters to iteratively apply steps 1) and 2) above to the updated problem until all time slots have been processed; E0′=E max ,

[0017] n max ′=n max -i1.

[0018] The principle of this invention is as follows: Since the problem under study is a convex optimization of energy harvesting, by modifying the tunneling strategy, the Lagrangian function is obtained using environmental constraints, and the KKT conditions are used to obtain the solution structure of the optimal solution for the energy consumed in each time slot. The tunneling algorithm is improved using the solution structure, thereby obtaining the optimal solution for the energy used in each time slot, that is, the energy consumption strategy of the whole process.

[0019] The advantage of this invention compared to the prior art is that it uses a larger objective function compared to previously proposed tunneling strategies. Attached Figure Description

[0020] Figure 1 This is the time-slot energy arrival model of the present invention.

[0021] Figure 2 This invention relates to an energy distribution strategy within an energy tunnel. Detailed Implementation

[0022] We consider a time-slotted energy arrival model, where energy arrives randomly in time, such as... Figure 1 As shown. All time intervals have the same length. We assume that at time 0, the battery has an initial energy of E0 units, E max Let E be the battery capacity. The energy collected in a given time slot is given by the saturation soft constraint, and the energy arriving in each time slot is E. s We have s = 1, 2, ..., n+1. We consider the energy flow between time slots that satisfy the hard constraints of causality and the soft constraints of saturation.

[0023] To better utilize randomly arriving harvested energy to execute tasks on the processor, the QoS of tasks on embedded systems must be maximized under several practical constraints. These constraints include:

[0024] Energy causality (hard constraint): The available energy for processing tasks in each time slot i is finite, determined by the energy available in the last time slot s. i-1 The energy at the end is determined. It's impossible to utilize energy that hasn't yet arrived, nor is it possible to utilize the energy of the present moment. s It is the energy consumed by each time slot task.

[0025]

[0026] Energy saturation (soft constraint): There is an energy capacity constraint on the available energy for task processing. It requires that the remaining energy at the end of the last time slot plus the energy arriving at that time slot be less than the battery's storage capacity; otherwise, energy will overflow from the battery, leading to energy inefficiency and a suboptimal solution. This is not a hard constraint.

[0027]

[0028] Optimal resource allocation refers to maximizing the benefits of an energy supply system within a given timeframe and under certain constraints. Therefore, this problem can be formulated as follows:

[0029]

[0030] The objective function is an increasing convex function with respect to p.

[0031] The following considers energy allocation in two scenarios.

[0032] 1. One-dimensional energy allocation considering only causal hard constraints and saturation soft constraints.

[0033] As can be seen from the above analysis, under the constraints of causal hard constraints and saturation soft constraints, p is allocated to time slots with increasing convex objective functions.

[0034] Reference [1] proposes a tunnel policy that determines the upper bound of the length of the first constant power allocation and then iteratively processes the remaining time slots "until" the last time slot. We call the method proposed in [1] the "tunnel policy" (A1). However, we find that the tunnel policy always selects the maximum applicable range of the time slot as the constant power range, which has some problems. The tunnel policy takes p0[n] as the upper bound, p max [n] is the lower bound, n ub The upper time slot bound of constant power allocation

[0035]

[0036] However, in certain extreme cases, this can lead to a suboptimal solution. For example, there might be a solution like... Figure 2 The energy harvesting case is shown. We can see that there is Scheme 1, which first allocates power using the blue power allocation line in time slots 1 and 2, and then uses the green power allocation line in time slots 3 and 4. If we use Scheme 2, allocating power using the blue line in time slot 1, and then using the red line in time slots 2 through 4, the objective function will be greater than Scheme 1. We will temporarily disregard the allocation after time slot 4. Scheme 1 is a "tunneling strategy." Therefore, we can see that the tunneling strategy is suboptimal in some cases. This patent will provide an optimal solution to the one-dimensional power allocation problem, maximizing the objective function.

[0037] Since the above problem is a convex optimization problem, where the objective function is an increasing convex function with respect to p and has several affine function constraints, we use the Karush-Kuhn-Tucher (KKT) optimality conditions to analyze this problem. We define a Lagrangian function L for any λ1≥0, u1≥0.

[0038]

[0039] Where F(·) is the expression relative to p in Definition 1. s The objective function is an increasing convex function. We apply the KKT optimality condition to the Lagrange function, and then we have the following equation.

[0040]

[0041] λ1≥0, u1≥0,

[0042]

[0043]

[0044] (1), (2).

[0045] Optimal power allocation expressed in terms of Lagrange multipliers for

[0046]

[0047] g represents F(·) with respect to p s The partial derivative function (decreasing function) is the inverse function of the Lagrange multiplier, but the Lagrange multipliers are difficult to determine at once because they are numerous and coupled together. Therefore, we consider using a solution structure to provide a fairly simple offline solution method.

[0048] Based on the complementary relaxation condition, the Lagrange multipliers under different conditions are analyzed.

[0049] when When λ1≥0, u1=0; when When λ1=0, u1≥0; when and At that time, λ1 = 0, u1 = 0.

[0050] We observed in (3) The value increases with increasing λ1 and with increasing u1. However, when constraints (1) or (2) are valid, λ1 and u1 may still be zero. Therefore, the activity of constraint (1) or constraint (2) is a necessary condition for λ1 and u1 to be positive. We must give sufficient conditions for u1 or λ1 to be 0 and sufficient conditions for u1 or λ1 to be greater than 0, especially when the longest feasible constant power given by the tunneling strategy (A1) simultaneously hits the upper and lower limits.

[0051] Theorem 1: When The power increases during time slot s1, where l = l ueff

[0052] , l ueff =max{l u1 , l u2 , ..., l ueff}, l u1 , l u2 , ..., l ueff It is the number of time slot indicators that the distribution line touches the longest available tunnel upper limit. If there is also a time slot indicator number that touches the lower boundary of the tunnel... λ1 ,l λ2 ,…,l λ′ , l λ ,≤l ueff ,So

[0053] Otherwise, the power only decreases in time slot s1, and l = l λeff , l λeff ={l λ1 ,l λ2 ,…,l λeff}, l λ1 ,l λ2 , ..., l λeff It is the number of time slot indicators that the distribution line touches the longest available tunnel lower limit.

[0054] If there is also a time slot indicator number that touches the upper limit of the tunnel... u1 , l u2, …, l u′ , l u′ ≤l λeff ,

[0055] An energy allocation method for maximizing the utility of a stochastic energy arrival conditionally monotonically increasing convex function system, namely the Effective Encountering Bound Policy (EEBP, A2), is characterized by the following steps, considering only causal and saturation constraints:

[0056] 1) When

[0057] l ueff =max{l u1 , l u2 ,..,l ueff ], l=l u1 , l u2 , ..., l ueff It is the set of time slots where p1 touches the upper bound of the longest available channel. The last time slot is taken as the valid upper bound, and then... That is, under the saturation soft constraint condition, all multipliers before s1 are 0; collect data from time slot 1 to time slot s = l. ueff The slope p1 = p0[l ueff The energy of ], where n1 = l ueff ;

[0058] 2) Otherwise, l λeff =max{l λ1 , l λ2 , ..., l λeff}, l=l λ1 .l λ2 ,...,l λeff l = l λ1 ,lλ2 ,...,l λeff It is the set of time slots where p1 touches the lower bound of the longest available channel. The last time slot is taken as the valid lower bound touch, and then... The multipliers are all 0 under the hard constraint of causality, meaning that all multipliers before s1 are 0; collect data from time slot 1 to time slot l = l. λeff The slope p1 = p max [l λeff The energy of ], n1 = l λeff ;

[0059] 3) Use the modified and updated parameters to iteratively apply steps 1) and 2) above to the updated problem until all time slots have been processed; E0′=E max ,

[0060] n max ′=n max -i1.

[0061] We present several experiments to evaluate the performance of the proposed algorithm.

[0062] The simulation settings are shown in Table 1, and the tunnel parameters are given in Table 2.

[0063] If option A2 is used:

[0064] In the first round, the most effective time slot for the allocation line to touch the upper edge is s2. Time slots s1 and s3, which touch the upper edge of the tunnel before and after s2, are ineffective. We allocate energy p to each time slot in the first two time slots. s =8, where s = 1, 2, n1 = 2, i1 = s2, E′0 = 0.

[0065] In the second round, we continue to calculate the allocated energy in subsequent time slots, and the updated tunnel parameters are given in Table 3. In time slot s′3, the allocation line touches both the upper and lower edges of the tunnel; in fact, this is because we must use all the energy in the last time slot.

[0066] If we use solution A1:

[0067] In the first round, according to Table 2, the longest available channel terminates on s3, and we allocate p in the first three time slots. s =8 energy, and the remaining parameters are s = 1, 2, 3, n1 = 3, i1 = s3, E′0 = 5.

[0068] In the second round, the energy allocation for subsequent time slots is calculated, and the updated tunneling parameters are given in Table 4. This is also because we must use all the energy in the last time slot. The energy allocation for time slots 4 and 5 is 15.

[0069] Table 1 Simulation Settings

[0070] <![CDATA[E max ]]> <![CDATA[E0]]> <![CDATA[E1]]> <![CDATA[E2]]> <![CDATA[E3]]> <![CDATA[E4]]> 20 8 8 13 15 10

[0071] Table 2 First Round Tunnel Parameters

[0072] slot <![CDATA[p0]]> <![CDATA[p max <!-- 5 -->]]> 1 8 (8+8-20) / 1＝-4 2 (8+8) / 2＝8 (8+8+13-20) / 2＝4.5 3 (8+8+13) / 3＝9.7 (8+8+13+15-20) / 3＝8 4 (8+8+13+15) / 4＝11 (8+8+13+15+10-20) / 4＝8.5 5 (8+8+13+15+10) / 5＝10.8 (8+8+13+15+10) / 5＝10.8

[0073] Table 3 shows the tunnel parameters for the second round of the A2 algorithm.

[0074]

[0075] Table 4 shows the tunnel parameters for the second round of the A1 algorithm.

[0076] slot <![CDATA[p0]]> <![CDATA[p max ]]> 4-3 15 (15+10-20) / 1＝5 5-3 (15+10) / 2＝12.5 (15+10) / 2＝12.5

Claims

1. A method of energy allocation for maximizing the system utility of a set of random energy arrival condition monotonically increasing convex functions under only causality and saturation constraints, using an effective encountering bound policy (EEBP), characterized by The method comprises the following steps: First, the symbols used and the problem model are explained; Assuming initially E0 units of energy, E max is the battery capacity; E k is the energy absorbed by each time slot, measured at the end of each time slot, k is the time slot number, k = 1,..., N + 1; The following is the calculation method of the tunnel strategy, P[n] = [p max [n], p0[n]] = {p | p max [n] ≤ p ≤ p0[n]}, n is the time slot number; n ub is calculated using the existing geometric programming method, and the maximum time slot of the solution is allocated in the energy allocation tunnel; Energy causality constraint: the available energy for a processing task at each time slot i is limited by the last time slot s i-1 Energy decision at the end; it is not possible to exploit energy that has not yet arrived, nor the energy of the present time slot; p s is the energy consumed by each time slot task Energy saturation constraint: there is an energy capacity constraint on the available energy for task processing; it is required that the remaining energy at the end of the last time slot plus the energy arriving at that time slot is less than the storage capacity of the battery; otherwise, energy will overflow from the battery, resulting in low energy efficiency, which is a suboptimal solution, which is not a hard constraint; The optimal resource allocation is to maximize the benefit of the energy supply system under certain constraints within a certain time; therefore, this problem can be formulated as maximizing the convex function F(p s ); Using Karush-Kuhn - Tucher (KKT) optimality conditions to analyze this problem, define the Lagrangian function L with respect to any λ1≥ 0, u1≥ 0, F(·) is an increasing convex objective function on the energy p consumed per time slot s ; u1 is the Lagrangian multiplier corresponding to the saturation constraint for time slot l, λ1 is the Lagrangian multiplier corresponding to the causality constraint for time slot 1; l u1 is the time slot number at which the first edge is encountered, l u2 is the time slot number at which the second edge is encountered, and so on. 1) When l ueff = max{ l u1 , l u2 ,..., l ueff ], l = l u1 , l u2 , …, l ueff is the set of slots that p1 touches the upper bound of the longest available channel, taking the last slot as the effective touch upper bound, after which that is, the multipliers before s1 under the saturation constraint condition are all 0; the energy of the slope p1 = p0[l ueff ] from slot 1 to slot s = l ueff is collected, where n1 = l λeff ; 2) otherwise, l λeff = max{ l λ1 , l λ2 ,..., l λeff}, l = l λ1 , l λ2 ,..., l λeff is the set of time slots that pl touches the lower bound of the longest available channel, taking the last time slot as the valid touch lower bound, after is 0, that is, all the multipliers before sl are 0 under the causality constraint condition; the energy of the slope pl = p max [l λeff ] from time slot 1 to time slot l = l λeff is collected, n1 = l max ; 3) using the modified updated parameters, iterate through the updated problem using the above steps 1) and 2) until all time slots are processed; E0' = E0- E max ,

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