Online Synchronous Policy Iteration based on Concurrent Learning to solve continuous-time optimal control problem

To intercept a maneuvering target with a predetermined impact angle, a computational intelligence guidance law was proposed in this paper. Based on the theory of two-player zero-sum differential games, this problem is resolved efficiently by solving the Hamilton–Jacobi–Isaacs (HJI) equation. The Nash equilibrium solution of HJI equation can be solved with a policy iteration (PI) algorithm. Instead of using the offline PI algorithm, an online PI algorithm is introduced, in which the disturbance and control policies can be updated simultaneously. It can be proved that the online PI algorithm is a replacement for Newton’s iterative algorithm, the convergence of which is ensured by Kantorovich’s theorem. In the scenario of missiles intercepting targets, an adaptive critic structure based on a neural network (NN) is proposed to implement the online PI algorithm. Only one critic NN approximator is used in the PI algorithm to calculate a value function and the approximate Nash equilibrium solution. It is not necessary to acquire the exact internal dynamics information of nonlinear systems on the basis of online data sampling. The effectiveness of the computational intelligence guidance law is proven by simulation results.

Off-policy algorithm based Hierarchical optimal control for completely unknown dynamic systems

This article presents a nearly optimal solution to the cooperative formation control problem for large-scale multiagent system (MAS). First, multigroup technique is widely used for the decomposition of the large-scale problem, but there is no consensus between different subgroups. Inspired by the hierarchical structure applied in the MAS, a hierarchical leader-following formation control structure with multigroup technique is constructed, where two layers and three types of agents are designed. Second, adaptive dynamic programming technique is conformed to the optimal formation control problem by the establishment of performance index function. Based on the traditional generalized policy iteration (PI) algorithm, the multistep generalized policy iteration (MsGPI) is developed with the modification of policy evaluation. The novel algorithm not only inherits the advantages of high convergence speed and low computational complexity in the generalized PI algorithm but also further accelerates the convergence speed and reduces run time. Besides, the stability analysis, convergence analysis, and optimality analysis are given for the proposed multistep PI algorithm. Afterward, a neural network-based actor-critic structure is built for approximating the iterative control policies and value functions. Finally, a large-scale formation control problem is provided to demonstrate the performance of our developed hierarchical leader-following formation control structure and MsGPI algorithm.

This studies the infinite horizon optimal control problem for a class of continuous‐time systems subjected to multiplicative noises and Markovian jumps by using a data‐driven policy iteration algorithm. The optimal control problem is equivalent to solve a stochastic coupled algebraic Riccatic equation (CARE). An off‐line iteration algorithm is first established to converge the solutions of the stochastic CARE, which is generalised from an implicit iterative algorithm. By applying subsystems transformation (ST) technique, the off‐line iterative algorithm is decoupled into N parallel Kleinman's iterative equations. To learn the solution of the stochastic CARE from N decomposed linear subsystems data, an ST‐based data‐driven policy iteration algorithm is proposed and the convergence is proved. Finally, a numerical example is given to illustrate the effectiveness and applicability of the proposed two iterative algorithms.

Optimal [formula omitted] tracking control of nonlinear systems with zero-equilibrium-free via novel adaptive critic designs

In this chapter, by using neural network (NN)-based online learning optimal control approach, a decentralized control strategy is developed to stabilize a class of continuous-time large-scale interconnected nonlinear systems . It is proven that the decentralized control strategy of the overall system can be established by adding appropriate feedback gains to the optimal control laws of the isolated subsystems . Then, an online policy iteration (PI) algorithm is developed to solve the Hamilton–Jacobi–Bellman equations related to the optimal control problem. By constructing a set of critic NNs, the cost functions can be obtained by NN approximation, followed by the control laws. Furthermore, as a generalization, an NN-based decentralized control law is developed to stabilize the large-scale interconnected nonlinear systems using an online model-free integral PI algorithm. The model-free PI approach can solve the decentralized control problem for large-scale interconnected nonlinear systems with unknown dynamics. Finally, two simulation examples are provided to illustrate the effectiveness of the present decentralized control scheme.

This article is concerned with the asynchronous $H_{\infty }$ control design based on model-free policy iteration (PI) algorithm for a class of discrete-time hidden Markov jump system, where a hidden Markov model is developed to characterize the asynchronous phenomenon between the controller modes and the system modes. A pair of zero-sum asynchronous control and disturbance strategies are constructed to achieve a tradeoff between value function and control performance. The presented approach shows two pivotal aspects: 1) the asynchronous PI algorithm is not dependent on strict temporal alignment between the controller and the system's dynamics, enhancing flexibility of the control scheme and 2) it relies on the collected data to solve the algebraic Reccati equation iteratively, which avoids the need for system-internal and transfer probability information, and circumvents the interference of coupled terms. Subsequently, it is verified that the designed PI algorithm monotonically converges to an optimal solution and the system based on this optimal solution is stochastically stable in the mean-square sense. Finally, the effectiveness of this approach is validated by conducting a simulation experiment on a DC motor device system.

Adaptive nearly optimal control for a class of continuous-time nonaffine nonlinear systems with inequality constraints

Multiagent Markov Decision Processes provide a rich framework to model problems of multiagent sequential decision under uncertainty, as in robotics. However, when the state space is also factored and of high dimension, even dedicated solution algorithms (exact or approximate) do not apply when the dimension of the state space and the number of agents both exceed 30, except under strong assumptions about state transitions or value function. In this paper we introduce the F\(^3\)MDP framework and associated approximate solution algorithms which can tackle much larger problems. An F\(^3\)MDP is a collaborative multiagent MDP whose state space is factored, reward function is additively factored and solution policies are constrained to be factored and can be stochastic. The proposed algorithms belong to the family of Policy Iteration (PI) algorithms. On small problems, where the optimal policy is available, they provide policies close to optimal. On larger problems belonging to the subclass of GMDPs they compete well with state-of-the-art resolution algorithms in terms of quality. Finally, we show that our algorithms can tackle very large F\(^3\)MDPs, with 100 agents and a state space of size \(2^{100}\).KeywordsMultiagent markov decision processesPolicy gradientInference in graphical models

This paper studies the online adaptive optimal controller design for a class of nonlinear systems through a novel policy iteration (PI) algorithm. By using the technique of neural network linear differential inclusion (LDI) to linearize the nonlinear terms in each iteration, the optimal law for controller design can be solved through the relevant algebraic Riccati equation (ARE) without using the system internal parameters. Based on PI approach, the adaptive optimal control algorithm is developed with the online linearization and the two-step iteration, i.e., policy evaluation and policy improvement. The convergence of the proposed PI algorithm is also proved. Finally, two numerical examples are given to illustrate the effectiveness and applicability of the proposed method.

ABSTRACTIn this article, the initial excitation‐based inverse reinforcement learning methods are presented for continuous‐time linear non‐zero‐sum games. The policy iteration and value iteration algorithms are presented for the inverse reinforcement learning problems, and an online‐verifiable initial excitation condition is given to guarantee the convergence of the presented algorithms. Comparing with the traditional inverse reinforcement learning algorithms for linear non‐zero‐sum games, the presented algorithms relax the requirement on data‐storage mechanism. Furthermore, the requirement on the initial stabilizing state feedback matrices is relaxed in the presented initial excitation‐based value iteration algorithm. The properties of the presented initial excitation‐based policy iteration and value iteration algorithms are analyzed. Simulation results show the efficiency of the presented algorithms.

This paper studies the stochastic optimal control problem with additive and multiplicative noise via reinforcement learning (RL) and approximate/adaptive dynamic programming (ADP). Using Itô calculus, a policy iteration algorithm is derived in the presence of both additive and multiplicative noise. It is shown that the expectation of the approximated cost matrix is guaranteed to converge to the solution of certain algebraic Riccati equation that gives rise to the optimal cost value. Furthermore, the covariance of the approximated cost matrix can be reduced by increasing the length of time interval between two consecutive iterations. Finally, the efficiency of the proposed ADP methodology is illustrated in a numerical example.

A novel policy iteration algorithm, called the continuous-time time-varying (CTTV) policy iteration algorithm, is presented in this paper to obtain the optimal control laws for infinite horizon CTTV nonlinear systems. The adaptive dynamic programming (ADP) technique is utilized to obtain the iterative control laws for the optimization of the performance index function. The properties of the CTTV policy iteration algorithm are analyzed. Monotonicity, convergence, and optimality of the iterative value function have been analyzed, and the iterative value function can be proven to monotonically converge to the optimal solution of the Hamilton-Jacobi-Bellman (HJB) equation. Furthermore, the iterative control law is guaranteed to be admissible to stabilize the nonlinear systems. In the implementation of the presented CTTV policy algorithm, the approximate iterative control laws and iterative value function are obtained by neural networks. Finally, the numerical results are given to verify the effectiveness of the presented method.

This paper introduces an online fault-tolerant control method for nonlinear time-delay systems with actuator faults using a policy iteration algorithm. A new performance index function is proposed to account for time-delay states, from which control laws are derived. The approach combines policy iteration with a fault compensator, solving the Hamilton-Jacobi-Bellman equation associated with this innovative value function via a critic neural network. Actuator faults are reconstructed for online fault compensation without the need for fault detection and isolation. The Lyapunov functional analysis demonstrates the closed-loop system's asymptotic stability in the presence of actuator faults and time-delay states. Simulation results validate the effectiveness of the proposed fault compensation strategy. The key contribution of this paper is the incorporation of time-delay states into the value function of the policy iteration algorithm, addressing the problem of fault compensation in nonlinear time-delay systems.

We are honored to organize this special issue of Neural Computation and Applications, based on contributions to the Ninth International Symposium on Neural Networks (ISNN 2012) held on July 11–14, 2012, in Shenyang, China. Evaluated by the contributions and the recommendation of ISNN 2012 organizers, 22 papers were selected for the further review process with their extended form. Each paper has been reviewed thoroughly by three independent experts in related research area. We are very grateful for the hard work of the reviewers, which help to facilitate the outcome of this special issue with greatly improved quality of the contributions. Finally, 20 papers are accepted, to be introduced as follows. In brief, the contributions of this special issue can be roughly classified into three major categories: data-based control, data-based optimization, and data-based modeling. In each category, not only the theoretical foundation is analyzed, but also some prospective applications are demonstrated. In this introduction, we like to borrow some ideas from the contributions, such as hierarchical, and cluster as the subsidiary category idea. The first category consisting of 6 papers is devoted to the data-based control and applications area, by which an optimal or near-optimal control can be derived from the input and output data. The first 4 papers focus on the hot research direction, adaptive dynamic programming and reinforcement learning (ADPRL), and the remaining 2 papers relate to iterative learning control and optimal control. Derong Liu et al. develop an online algorithm based on policy iteration for continuous-time optimal control with infinite horizon cost for nonlinear systems. In the proposed method, a discount value function is employed, which is considered to be a more general case for optimal control problems. Meanwhile, without knowledge of the internal system dynamics, the algorithm can converge uniformly online to the optimal solution of the modified Hamilton– Jacobi–Bellman equation. By means of two neural networks, the algorithm is able to find suitable approximations of both the optimal control and the optimal cost. Dual iterative adaptive dynamic programming for a class of discrete-time nonlinear systems with time-delays is investigated by Qinglai Wei et al. Dual iterative ADP algorithm is introduced to obtain the optimal solutions of the optimal performance index function and control, where in each iteration, the performance index function and the system states are both updated. Convergence analysis is presented to prove the performance index function to reach D. Zhao (&) State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China e-mail: Dongbin.zhao@ia.ac.cn