Yuan Tan

The constrained output regulation problems of discrete-time linear systems are studied under the model predictive control framework. The unique feature of the proposed control approach lies in addressing the technical challenges related to recursive feasibility of the optimization problem and stability of the closed-loop system posed by exogenous signal estimation and estimation errors. First, the original system is transformed into a new dynamic system by means of regulator equations and disturbance observer techniques, which enables output regulation problems to be reformulated into state stabilization problems. For the constraints reconstruction, a robust positively invariant set sequence is then skillfully designed to provide bounds for the deviations between the transformed system and its corresponding nominal system. A hierarchical control strategy is utilized that comprises two components: the first is an optimal controller designed to stabilize the nominal system with tightened constraints, while the second is a feedback controller used to restrain the deviations between the nominal and transformed systems. Constraints satisfaction can be directly verified through set operations, and the theoretical guarantees are ensured through rigorous theoretical analysis. Furthermore, the proposed framework also encompasses the output-feedback case. The numerical simulations demonstrate the effectiveness of the proposed method in addressing constrained output regulation problems, even when the exogenous signal is partially available.

Inspired by the concept of recently proposed dual control for exploration and exploitation, this article presents a multistep dual control for exploration and exploitation with guaranteed convergence in search for autonomous sources. To deal with an unknown source position and environment, the proposed dual control algorithm faces significant challenges in demonstrating its recursive feasibility and convergence. With the help of the properties of Bayesian estimators, we redesign a multistep dual control for exploitation and exploration algorithm with necessary terminal ingredients and show that the recursive feasibility and the convergence of the modified dual control algorithm are guaranteed. Two simulation scenarios are conducted, which demonstrate that the proposed algorithm outperforms the stochastic model-predictive control approach and the informative path planning approach in terms of searching successful rates and efficiency.

In this work, we propose a distributionally robust stochastic model predictive control (DR-SMPC) algorithm to address the problem of multiple two-sided chance constrained discrete-time linear systems corrupted by additive noise. The prevalent mechanism to cope with two-sided chance constraints is the so-called risk allocation approach, which conservatively approximates the two-sided chance constraints with two single chance constraints by applying Bool's inequality. In this proposed DR-SMPC framework, an exact second-order cone approach is adopted to abstract the multiple two-sided chance constraints by considering the first and second moments of the noise. With the proposed DR-SMPC algorithm, the worst-case probability of violating safety constraints is guaranteed to be within a pre-specified maximum value. By flexibly adjusting this pre-specified maximum probability, the feasible region of the initial state can be increased for the SMPC problem. The recursive feasibility and convergence of the proposed DR-SMPC are rigorously established by introducing a binary initialization strategy for the nominal state. A simulation study of a single spring and double mass system was conducted to demonstrate the effectiveness of the proposed DR-SMPC algorithm.

Two stochastic model predictive control (SMPC) algorithms, which are referred to as distributionally robust model predictive control (DRMPC) algorithms, are proposed in this paper for a class of discrete linear systems with unbounded noise. Participially, chance constraints are imposed on both of the state and control, which makes the problem more challenging. Inspired by the ideas from distributionally robust optimization, two deterministic convex reformulations are proposed for tackling the chance constraints. Rigorous computational complexity analysis is carried out to compare the two proposed algorithms with the existing methods. Recursive feasibility and convergence are proved. Simulation results are provided to show the effectiveness of the proposed algorithms.