Robust Output Feedback MPC for LPV Systems Using Interval Observers

Abstract

This work addresses the problem of robust output feedback model predictive control for discrete-time, constrained, linear parameter-varying systems subject to (bounded) state and measurement disturbances. The vector of scheduling parameters is assumed to be an unmeasurable signal taking values in a given compact set. The proposed controller incorporates an interval observer, that uses the available measurement to update the setmembership estimation of the states, and an interval predictor, used in the prediction step of the MPC algorithm. The resulting MPC scheme offers guarantees on recursive feasibility, constraint satisfaction, and input-to-state stability in the terminal set. Furthermore, this novel algorithm shows low computation complexity and ease of implementation (similar to conventional MPC schemes).

An Interval Observer for Continuous-Time Persidskii Systems

“…To illustrate the 6) for a Lotka-Volterra model: x(t), x(t), x(t) versus time t efficiency of the proposed interval observer, it was applied to a Lotka-Volterra model. Development of these results to interval prediction and model predictive control design as in [41], [42] can be considered as a direction for future research.…”

Robust interval predictive tracking control for constrained and perturbed unicycle mobile robots

“…Therefore, taking into account (10) and substituting (17) in (7), the dynamics of the system on the sliding surface is given by $$$$ \dot{e}=\left[{A}_0+\sum \limits_{j=1}^4{\alpha}_j\left({\rho}_1\right){\overset{\widetilde }{A}}_j\right]e+B{u}_0, $$$$ where $$$ {\overset{\widetilde }{A}}_j=\left({I}_3- BG\right){A}_j $$$. Then, according to Lemma 1 and Reference 35, it follows that $$$$ -\overline{A}{\underset{\_}{e}}^{-}-\underset{\_}{A}{\overline{e}}^{+}\le \sum \limits_{j=1}^4{\alpha}_j\left({\rho}_1\right){\overset{\widetilde }{A}}_je\le \overline{A}{\overline{e}}^{+}+\underset{\_}{A}{\underset{\_}{e}}^{-}, $$$$ where $$$ \overline{A}={\sum}_{j=1}^4{\overset{\widetilde }{A}}_j^{+} $$$, …”

Interval Observation and Control for Continuous-Time Persidskii Systems

“…2, the results of simulation are shown for the controlled system with x(0) = [2.2 0.4] ⊤ (solid lines correspond to the trajectories of the system, dot and dash curves represent the lower and upper interval estimates, respectively). As we can see, the proposed interval observer (6) generates accurate estimates and the control (9) regulates the system to a vicinity of the origin in spite of the influence of d. Since all admissible trajectories are evaluated by (6), the control ( 9) can be complemented with a model predictive one as in [49], [50], which can be a direction of future research.…”