Adaptive near-optimal neuro controller for continuous-time nonaffine nonlinear systems with constrained input

Adaptive dynamic programming-based hierarchical decision-making of non-affine systems

In this paper, the problem of multiplayer hierarchical decision-making problem for non-affine systems is solved by adaptive dynamic programming. Firstly, the control dynamics are obtained according to the theory of dynamic feedback and combined with the original system dynamics to construct the affine augmented system. Thus, the non-affine multiplayer system is transformed into a general affine form. Then, the hierarchical decision problem is modeled as a Stackelberg game. In the Stackelberg game, the leader makes a decision based on the information of all followers, whereas the followers do not know each other's information and only obtain their optimal control strategy based on the leader's decision. Then, the augmented system is reconstructed by a neural network (NN) using input-output data. Moreover, a single critic NN is used to approximate the value function to obtain the optimal control strategy for each player. An extra term added to the weight update law makes the initial admissible control law no longer needed. According to the Lyapunov theory, the state of the system and the error of the weights of the NN are both uniformly ultimately bounded. Finally, the feasibility and validity of the algorithm are confirmed by simulation.

Adaptive Learning and Sampled-Control for Nonlinear Game Systems Using Dynamic Event-Triggering Strategy

Static event-triggering-based control problems have been investigated when implementing adaptive dynamic programming algorithms. The related triggering rules are only current state-dependent without considering previous values. This motivates our improvements. This article aims to provide an explicit formulation for dynamic event-triggering that guarantees asymptotic stability of the event-sampled nonzero-sum differential game system and desirable approximation of critic neural networks. This article first deduces the static triggering rule by processing the coupling terms of Hamilton-Jacobi equations, and then, Zeno-free behavior is realized by devising an exponential term. Subsequently, a novel dynamic-triggering rule is devised into the adaptive learning stage by defining a dynamic variable, which is mathematically characterized by a first-order filter. Moreover, mathematical proofs illustrate the system stability and the weight convergence. Theoretical analysis reveals the characteristics of dynamic rule and its relations with the static rules. Finally, a numerical example is presented to substantiate the established claims. The comparative simulation results confirm that both static and dynamic strategies can reduce the communication that arises in the control loops, while the latter undertakes less communication burden due to fewer triggered events.

Event-based optimal guidance laws design for missile-target interception systems using fuzzy dynamic programming approach

In this paper, the guidance system with unknown dynamics is modeled as a partially unknown zero-sum differential game system. Then, a periodic event-triggered optimal control algorithm is designed to interception target under a plug-n-play framework. To realize this algorithm, generalized fuzzy hyperbolic models are employed to construct the identifier-critic structure, where the online identifier is used to estimate unknown dynamics, meanwhile, the generalized fuzzy hyperbolic models-based critic network is utilized to approximate the cost function. Note that plug-n-play framework lets both the designed identifier and critic network work simultaneously, in other words, the prior system information is no longer required, which simplifies the network structure. Using the Lyapunov function method, the approximate optimal control strategy and corresponding weight updating laws are derived to guarantee that the closed-loop system and weight approximation errors are uniformly ultimately bounded, where an additional function is added to weight updating laws to release the requirement for admissible initial control. Finally, to compare the intercept effects and the utilization ratio of communication resources of the periodic event-triggered control algorithm and the common adaptive dynamic programming algorithm, the missile interception system is introduced as an example.

Adaptive Optimal Control for Unknown Constrained Nonlinear Systems With a Novel Quasi-Model Network

A policy-iteration-based algorithm is presented in this article for optimal control of unknown continuous-time nonlinear systems subject to bounded inputs by utilizing the adaptive dynamic programming (ADP). Three neural networks (NNs), called critic network, actor network, and quasi-model network, are utilized in the proposed algorithm to give approximations of the control law, the cost function, and the function constituted by partial derivatives of value functions with respect to states and unknown input gain dynamics, respectively. At each iteration, based on the least sum of squares method, the parameters of critic and quasi-model networks will be tuned simultaneously, which eliminates the necessity of separately learning the system model in advance. Then, the control law is improved by satisfying the necessary optimality condition. Then, the proposed algorithm's optimality and convergence properties are exhibited. Finally, the simulation results demonstrate the availability of the proposed algorithm.