A dual-control effect preserving formulation for nonlinear output-feedback stochastic model predictive control with constraints

In this paper we propose a formulation for approximate constrained nonlinear output-feedback stochastic model predictive control. Starting from the ideal but intractable stochastic optimal control problem (OCP), which involves the optimization over output-dependent policies, we use linearization with respect to the uncertainty to derive a tractable approximation which includes knowledge of the output model. This allows us to compute the expected value for the outer functions of the OCP exactly. Crucially, the dual control effect is preserved by this approximation. In consequence, the resulting controller is aware of how the choice of inputs affects the information available in the future which in turn influences subsequent controls. Thus, it can be classified as a form of implicit dual control

Output Feedback Stochastic MPC with Hard Input Constraints

We present an output feedback stochastic model predictive controller (SMPC) for constrained linear time-invariant systems. The system is perturbed by additive Gaussian disturbances on state and additive Gaussian measurement noise on output. A Kalman filter is used for state estimation and an SMPC is designed to satisfy chance constraints on states and hard constraints on actuator inputs. The proposed SMPC constructs bounded sets for the state evolution and a tube-based constraint tightening strategy where the tightened constraints are time-invariant. We prove that the proposed SMPC can guarantee an infeasibility rate below a user-specified tolerance. We numerically compare our method with a classical output feedback SMPC with simulation results which highlight the efficacy of the proposed algorithm.Comment: IEEE American Control Conference (ACC) 2023, May 31 - June 2, San Diego, CA, US

Robust model predictive control under redundant channel transmission with applications in networked DC motor systems

In networked systems, intermittent failures in data transmission are usually inevitable due to the limited bandwidth of the communication channel, and an effective countermeasure is to add redundance so as to improve the reliability of the communication service. This paper is concerned with the model predictive control (MPC) problem by using static output feedback for a class of polytopic uncertain systems with redundant channels under both input and output constraints. By utilizing the min-max control approach combined with stochastic analysis, sufficient conditions are established to guarantee the feasibility of the designed MPC scheme that ensures the robust stability of the closed-loop system. In terms of the solution to an auxiliary optimization problem, an easy-to-implement MPC algorithm is proposed to obtain the desired sub-optimal control sequence as well as the upper bound of the quadratic cost function. Finally, to illustrate its effectiveness, the proposed design method is applied to control a networked direct current motor system

Optimal control of dynamical systems with time-invariant probabilistic parametric uncertainties

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Chemical Engineering, February 2018.Cataloged from PDF version of thesis. "September 2017." Handwritten on title page "February 2018."Includes bibliographical references (pages 117-121).The importance of taking model uncertainties into account during controller design is well established. Although this theory is well developed and quite mature, the worst-case uncertainty descriptions assumed in robust control formulations are incompatible with the uncertainty descriptions generated by commercial model identification software that produces time-invariant parameter uncertainties typically in the form of probability distribution functions. This doctoral thesis derives rigorous theory and algorithms for the optimal control of dynamical systems with time-invariant probabilistic uncertainties. The main contribution of this thesis is new feedback control design algorithms for linear time-invariant systems with time-invariant probabilistic parametric uncertainties and stochastic noise. The originally stochastic system of equations is transformed into an equivalent deterministic system of equations using polynomial chaos (PC) theory. In addition, the H2- and H[infinity symbol]-norms commonly used to describe the effect of stochastic noise on output are transformed such that the eventual closed-loop performance is insensitive to parametric uncertainties. A robustifying constant is used to enforce the closed-loop stability of the original system of equations. This approach results in the first PC-based feedback control algorithm with proven closed-loop stability, and the first PC-based feedback control formulation that is applicable to the design of fixed-order state and output feedback control designs. The numerical algorithm for the control design is formulated as optimization over bilinear matrix inequality (BMI) constraints, for which commercial software is available. The effectiveness of the approach is demonstrated in two case studies that include a continuous pharmaceutical manufacturing process. In addition to model uncertainties, chemical processes must operate within constraints, such as upper and lower bounds on the magnitude and rate of change of manipulated and/or output variables. The thesis also demonstrates an optimal feedback control formulation that explicitly addresses both constraints and time-invariant probabilistic parameter uncertainties for linear time-invariant systems. The H2-optimal feedback controllers designed using the BMI formulations are incorporated into a fast PC-based model predictive control (MPC) formulation. A numerical case study demonstrates the improved constraint satisfaction compared to past polynomial chaos-based formulations for model predictive control.by Dongying Erin Shen.Ph. D

Output feedback stable stochastic predictive control with hard control constraints

We present a stochastic predictive controller for discrete time linear time invariant systems under incomplete state information. Our approach is based on a suitable choice of control policies, stability constraints, and employment of a Kalman filter to estimate the states of the system from incomplete and corrupt observations. We demonstrate that this approach yields a computationally tractable problem that should be solved online periodically, and that the resulting closed loop system is mean-square bounded for any positive bound on the control actions. Our results allow one to tackle the largest class of linear time invariant systems known to be amenable to stochastic stabilization under bounded control actions via output feedback stochastic predictive control

An Extended Kalman Filter for Data-enabled Predictive Control

The literature dealing with data-driven analysis and control problems has significantly grown in the recent years. Most of the recent literature deals with linear time-invariant systems in which the uncertainty (if any) is assumed to be deterministic and bounded; relatively little attention has been devoted to stochastic linear time-invariant systems. As a first step in this direction, we propose to equip the recently introduced Data-enabled Predictive Control algorithm with a data-based Extended Kalman Filter to make use of additional available input-output data for reducing the effect of noise, without increasing the computational load of the optimization procedure