Simultaneous Nonlinear Model Predictive Control and State Estimation: Theory and Applications

As computational power increases, online optimization is becoming a ubiquitous approach for solving control and estimation problems in both academia and industry. This widespread popularity of online optimization techniques is largely due to their abilities to solve complex problems in real time and to explicitly accommodate hard constraints. In this dissertation, we discuss an especially popular online optimization control technique called model predictive control (MPC). Specifically, we present a novel output-feedback approach to nonlinear MPC, which combines the problems of state estimation and control into a single min-max optimization. In this way, the control and estimation problems are solved simultaneously providing an output-feedback controller that is robust to worst-case system disturbances and noise. This min-max optimization is subject to the nonlinear system dynamics as well as constraints that come from practical considerations such as actuator limits. Furthermore, we introduce a novel primal-dual interior-point method that can be used to efficiently solve the min-max optimization problem numerically and present several examples showing that the method succeeds even for severely nonlinear and non-convex problems. Unlike other output-feedback nonlinear optimal control approaches that solve the estimation and control problems separately, this combined estimation and control approach facilitates straightforward analysis of the resulting constrained, nonlinear, closed-loop system and yields improved performance over other standard approaches. Under appropriate assumptions that encode controllability and observability of the nonlinear process to be controlled, we show that this approach ensures that the state of the closed-loop system remains bounded. Finally, we investigate the use of this approach in several applications including the coordination of multiple unmanned aerial vehicles for vision-based target tracking of a moving ground vehicle and feedback control of an artificial pancreas system for the treatment of Type 1 Diabetes. We discuss why this novel combined control and estimation approach is especially beneficial for these applications and show promising simulation results for the eventual implementation of this approach in real-life scenarios

Robust economic model predictive control: recursive feasibility, stability and average performance

This thesis is mainly concerned with designing algorithms for Economic Model Predictive Control (EMPC), and analysis of its resulting recursive feasibility, stability and asymptotic average performance. In particular, firstly, in order to extend and unify the formulation and analysis of economic model predictive control for general optimal operation regimes, including steady-state or periodic operation, we propose the novel concept of a “control storage function” and introduce upper and lower bounds to the best asymptotic average performance for nonlinear control systems based on suitable notions of dissipativity and controlled dissipativity. As a special case, when the optimal operation is periodic, we present a new approach to formulate terminal cost functions. Secondly, aiming at designing a robust EMPC controller for nonlinear systems with general optimal regimes of operation, we present a tube-based robust EMPC algorithm for discrete-time nonlinear systems that are perturbed by disturbance inputs. The proposed algorithm minimizes a modified economic objective function, which considers the worst cost within a tube around the solution of the associated nominal system. Recursive feasibility and an a-priori upper bound to the closed-loop asymptotic average performance are ensured. Thanks to the use of dissipativity of the nominal system with a suitable supply rate, the closed-loop system under the proposed controller is shown to be asymptotically stable, in the sense that it is driven to an optimal robust invariant set. Thirdly, for the purpose of combining robust EMPC design with a state observer in a single pure economic optimization problem, we consider homothetic tube-based EMPC synthesis for constrained linear discrete time systems. Since, in practical systems, full state measurement is seldom available, the proposed method integrates a moving horizon estimator to achieve closed-loop stability and constraint satisfaction despite system disturbances and output measurement noise. In contrast to existing approaches, the worst cost within a single homothetic tube around the solution of the associated nominal system is minimized, which at the same time tightens the bound on the set of potential states compatible with past output and input data. We show that the designed optimization problem is recursively feasible and adoption of homothetic tubes leads to less conservative economic performance bounds. In addition, the use of strict dissipativity of the nominal system guarantees asymptotic stability of the resulting closed-loop system. Finally, to deal with the unknown nonzero mean disturbance and the presence of plant-model error, we propose a novel economic MPC algorithm aiming at achieving optimal steady-state performance despite the presence of plant-model mismatch or unmeasured nonzero mean disturbances. According to the offset-free formulation, the system's state is augmented with disturbances and transformed into a new coordinate framework. Based on the new variables, the proposed controller integrates a moving horizon estimator to determine a solution of the nominal system surrounded by a set of potential states compatible with past input and output measurements. The worst cost within a single homothetic tube around the nominal solution is chosen as the economic objective function which is minimized to provide a tightened upper bound for the accumulated real cost within the prediction horizon window. Thanks to the combined use of the nominal system and homothetic tube, the designed optimization problem is recursively feasible and less conservative economic performance bounds are achieved.Open Acces