Shimin Wang

Xinyang Wang, Hongwei Zhang, Shimin Wang et al.

Merely pursuing performance may adversely affect the safety, while a conservative policy for safe exploration will degrade the performance. How to balance the safety and performance in learning-based control problems is an interesting yet challenging issue. This paper aims to enhance system performance with safety guarantee in solving the reinforcement learning (RL)-based optimal control problems of nonlinear systems subject to high-relative-degree state constraints and unknown time-varying disturbance/actuator faults. First, to combine control barrier functions (CBFs) with RL, a new type of CBFs, termed high-order reciprocal control barrier function (HO-RCBF) is proposed to deal with high-relative-degree constraints during the learning process. Then, the concept of gradient similarity is proposed to quantify the relationship between the gradient of safety and the gradient of performance. Finally, gradient manipulation and adaptive mechanisms are introduced in the safe RL framework to enhance the performance with a safety guarantee. Two simulation examples illustrate that the proposed safe RL framework can address high-relative-degree constraint, enhance safety robustness and improve system performance.

Maobin Lu, Martin Guay, Telema Harry et al.

This paper investigates the robust output regulation problem of second-order nonlinear uncertain systems with an unknown exosystem. Instead of the adaptive control approach, this paper resorts to a robust control methodology to solve the problem and thus avoid the bursting phenomenon. In particular, this paper constructs generic internal models for the steady-state state and input variables of the system. By introducing a coordinate transformation, this paper converts the robust output regulation problem into a nonadaptive stabilization problem of an augmented system composed of the second-order nonlinear uncertain system and the generic internal models. Then, we design the stabilization control law and construct a strict Lyapunov function that guarantees the robustness with respect to unmodeled disturbances. The analysis shows that the output zeroing manifold of the augmented system can be made attractive by the proposed nonadaptive control law, which solves the robust output regulation problem. Finally, we demonstrate the effectiveness of the proposed nonadaptive internal model approach by its application to the control of the Duffing system.

Dong Liang, Martin Guay, Shimin Wang

In this paper, a bipartite output regulation problem is solved for a class of nonlinear multi-agent systems subject to static signed communication networks. A nonlinear distributed observer is proposed for a nonlinear exosystem with cooperation-competition interactions to address the problem. Sufficient conditions are provided to guarantee its existence and stability. The exponential stability of the observer is established. As a practical application, a leader-following bipartite consensus problem is solved for a class of nonlinear multi-agent systems based on the observer. Finally, a network of multiple pendulum systems is treated to support the feasibility of the proposed design. The possible application of the approach to generate specific Turing patterns is also presented.

Shimin Wang, Xiangyu Meng, Hongwei Zhang et al.

Knowledge-based leader-following synchronization of heterogeneous nonlinear multi-agent systems is a challenging problem since the leader's dynamic information is unknown to any follower node. This paper proposes a learning-based fully distributed observer for a class of nonlinear leader systems, which can simultaneously learn the leader's dynamics and states. This class of leader dynamics is rather general and does not require a bounded Jacobian matrix. Based on this learning-based distributed observer, we further synthesize an adaptive distributed control law for solving the leader-following synchronization problem of multiple Euler-Lagrange systems subject to an uncertain nonlinear leader system. The results are illustrated by a simulation example.