Periodic Event-Triggered Suboptimal Control With Sampling Period and Performance Analysis

Hamiltonian-Driven Adaptive Dynamic Programming With Approximation Errors

In this article, we consider an iterative adaptive dynamic programming (ADP) algorithm within the Hamiltonian-driven framework to solve the Hamilton-Jacobi-Bellman (HJB) equation for the infinite-horizon optimal control problem in continuous time for nonlinear systems. First, a novel function, "min-Hamiltonian," is defined to capture the fundamental properties of the classical Hamiltonian. It is shown that both the HJB equation and the policy iteration (PI) algorithm can be formulated in terms of the min-Hamiltonian within the Hamiltonian-driven framework. Moreover, we develop an iterative ADP algorithm that takes into consideration the approximation errors during the policy evaluation step. We then derive a sufficient condition on the iterative value gradient to guarantee closed-loop stability of the equilibrium point as well as convergence to the optimal value. A model-free extension based on an off-policy reinforcement learning (RL) technique is also provided. Finally, numerical results illustrate the efficacy of the proposed framework.

Event-Triggered ADP for Tracking Control of Partially Unknown Constrained Uncertain Systems

An event-triggered adaptive dynamic programming (ADP) algorithm is developed in this article to solve the tracking control problem for partially unknown constrained uncertain systems. First, an augmented system is constructed, and the solution of the optimal tracking control problem of the uncertain system is transformed into an optimal regulation of the nominal augmented system with a discounted value function. The integral reinforcement learning is employed to avoid the requirement of augmented drift dynamics. Second, the event-triggered ADP is adopted for its implementation, where the learning of neural network weights not only relaxes the initial admissible control but also executes only when the predefined execution rule is violated. Third, the tracking error and the weight estimation error prove to be uniformly ultimately bounded, and the existence of a lower bound for the interexecution times is analyzed. Finally, simulation results demonstrate the effectiveness of the present event-triggered ADP method.

Periodic Event-Triggered Output-Feedback Stabilization for Stochastic Systems

This article is devoted to explore the periodic event-triggered stabilization for continuous-time stochastic systems, and to develop analysis tools/methods for stochastic periodic event-triggered control. Notably, without real-time monitoring of system behavior as in the scenario with continuous event evaluation, it is critical to delicately estimate and govern the execution/sampling error to achieve the desired system performance. This, under stochastic effects, would be substantially challenging, since the behavior of the stochastic system is hard to predict and is disparate between trials even with the same initial conditions. In this article, a framework of global stabilization via periodic event-triggered output-feedback is established: 1) a criterion condition based on the ISS-Lyapunov function is presented for the feasibility of the desired event-triggered stabilization; 2) both the asymptotic stabilization and exponential stabilization are achieved for the systems, with delicately specifying the periodic event-triggering mechanism; and 3) the involved analysis, without applying the well-known Lyapunov theorems, can serve as a pattern from estimating sampling and execution errors to assess the closed-loop stability for stochastic periodic event-triggered control. Moreover, based on the established framework, we contribute the stabilizing controller design via periodic event-triggered output-feedback for a class of stochastic nonlinear systems.

Event-Triggered Adaptive Dynamic Programming for Unmatched Uncertain Nonlinear Continuous-Time Systems

In this article, an event-triggered adaptive dynamic programming (ADP) method is proposed to solve the robust control problem of unmatched uncertain systems. First, the robust control problem with unmatched uncertainties is transformed into the optimal control design for an auxiliary system. Subsequently, to reduce controller executions and save computational and communication resources, an event-triggering mechanism is introduced. By using a critic neural network (NN) to approximate the value function, novel concurrent learning is developed to learn NN weights, which avoids the requirement of an initial admissible control and the persistence of excitation condition. Moreover, it is proven that the developed event-triggered ADP controller guarantees the robustness of the uncertain system and the uniform ultimate boundedness of the NN weight estimation error. Finally, by using the F-16 aircraft and the inverted pendulum with unmatched uncertainties as examples, the simulation results show the effectiveness of the developed event-triggered ADP method.

Integral reinforcement learning based event-triggered control with input saturation

In this paper, a novel integral reinforcement learning (IRL)-based event-triggered adaptive dynamic programming scheme is developed for input-saturated continuous-time nonlinear systems. By using the IRL technique, the learning system does not require the knowledge of the drift dynamics. Then, a single critic neural network is designed to approximate the unknown value function and its learning is not subjected to the requirement of an initial admissible control. In order to reduce computational and communication costs, the event-triggered control law is designed. The triggering threshold is given to guarantee the asymptotic stability of the control system. Two examples are employed in the simulation studies, and the results verify the effectiveness of the developed IRL-based event-triggered control method.