Control Framework For Nonlinear Systems Research Articles

Guaranteed Closed-Loop Learning in Model Predictive Control

In this article, we propose a novel learning-based model predictive control framework for nonlinear systems which is able to guarantee closed-loop learning of the controlled system. We consider a cost function that combines a general economic cost with a user-defined learning cost function that aims at incentivizing learning of the unknown system. In particular, due to the finite horizon of the MPC scheme and to the presence of disturbances, the open-loop trajectory usually differs from the closed-loop one. Such a mismatch causes existing learning-based MPC schemes to only show a learning phase in the open-loop prediction, without providing any formal guarantee on the actual closed-loop learning. In this article, we show how existing MPC schemes can be easily modified in order to guarantee closed-loop learning of the system by including a suitable discount factor in the chosen learning cost function, and implementing an additional constraint in the original MPC scheme. We show that various techniques for online learning the system dynamics, such as kinky inference methods, Gaussian processes, or parametric approaches, can be used within the proposed general framework.

Predictor-based pose stabilization control for unmanned vehicles on SE(3) with actuator delay and saturation

This paper investigates the problem of predictor-based pose control framework for nonlinear systems on SE(3) subject to actuator delay and saturation. First, the exact predictive solution of the saturated pose-closed-loop system on SO(3)×R3 is proposed, based on which the predictor-based pose control law is established. Second, the integral predictive solution of the saturated pose-closed-loop system and the corresponding predictor-based control law are designed on SE(3) directly. Compared with the unmanned vehicles control on Euclidean space, the proposed control schemes not only guarantee that the predictor-based control laws are designed on nonlinear manifolds, but also ensure that the designed speed inputs satisfy the saturation constraint. Finally, the numerical simulations are provided to illustrate the effectiveness of the proposed theoretical results.

Nonlinear controllers for nonlinear systems with input nonlinearities

In this paper we develop an optimality-based nonlinear control framework for nonlinear systems with time-invariant sector-bounded memoryless input nonlinearities. Specifically, using an optimal nonlinear control framework we develop a family of globally stabilizing controllers parameterized by the cost functional that is minimized. Furthermore, it is shown that the control Lyapunov function guaranteeing closed-loop stability over a prescribed set of input nonlinearities is a solution to the steady-state Hamilton-Jacobi-Bellman equation for the controlled system and thus guarantees stability and performance.