(134b) Perspectives on Predictive Control with Dual Control Feature for Stochastic Systems

Model predictive control (MPC) has demonstrated exceptional success for high-performance control of complex systems in a wide range of applications [1,2]. However, systematic model uncertainty handling under closed-loop conditions remains a key theoretical and practical challenge in MPC. Even though standard MPC implementations on the basis of a nominal system model typically exhibit some degree of robustness to sufficiently small model uncertainty and system disturbances, marginal robust performance may not be deemed satisfactory in many practical situations. This consideration has led to development of robust MPC [3], as well as stochastic MPC when the probabilistic nature of uncertainties can be characterized [4], with the goal of guaranteeing robust stability and performance of the closed-loop system by explicitly accounting for system uncertainties. However, robust MPC and stochastic MPC are generally blind to the system changes and, therefore, their performance is limited by the quality of the a-priori specified nominal model and uncertainty descriptions. The time-varying nature of system dynamics (i.e., changes in plant and/or disturbance dynamics) tends to increase model uncertainty over time, which manifests itself in terms of inadequate model structure and/or parameter estimates. Increased model uncertainty generally results in degradation of the closed-loop control performance, as verified via performance monitoring and diagnosis (e.g., [5,6]). Thus, some form of online model adaptation must often be performed for retaining the control performance at an admissible level.

The problem of model uncertainty handling in model-based control lies at the intersection of the fields of robust control, adaptive control, and system identification for control. This talk draws on the seminal work of Feldbaum, which is widely regarded as the pioneering attempt that addressed the problem of model (parameter) uncertainty in model-based control design [7]. Feldbaum recognized the dual effect that input signals controlling an unknown system should have - the investigating effect to probe the system dynamics for actively learning about the system and the directing effect to effectively control the system dynamics. Control signals are said to have dual effect when, in addition to affecting the system states, they affect the uncertainty associated with the system states. The key notion of dual control hinges on compromising between the investigating and directing effects of the input signals, so that more system information can be gathered at the current time to enable achieving better control performance in future. In this talk, we will discuss the connection of the stochastic optimal control problem with dual feature to the stochastic dynamin programming problem, followed by an overview of the approximate solutions to the dual control problem in the context of predictive control of stochastic systems. We will then offer our perspectives for future research in this area in light of our recent results [8,9,10].

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[5] M. Zagrobelny, L. Ji, and J. B. Rawlings. Quis custodiet ipsos custodes? Annual Reviews in Control, 37:260-270, 2013.

[6] A. Mesbah, X. Bombois, M. Forgione, H. Hjalmarsson, and P.M.J. Van den Hof. Least costly closed-loop performance diagnosis and plant re-identification. International Journal of Control, pages 1-13, 2015.

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[8] C.A. Larsson, M. Annergren, H. Hjalmarsson, C.R. Rojas, X. Bombois, A. Mesbah, and P.E. Moden. Model predictive control with integrated experiment design for output error systems. In Proceedings of the European Control Conference, pages 3790-3795, Zurich, 2013.

[9] V. Bavdekar and A. Mesbah. Stochastic model predictive control with integrated experiment design for nonlinear systems. In Proceedings of the 11^th IFAC Symposium on Dynamics and Control of Process Systems (DYCOPS), Accepted, Trondheim, Norway, 2016.

[10] V. Bavdekar, V. Ehlinger, D. Gidon, and A. Mesbah. Stochastic predictive control with adaptive model maintenance. In Proceedings of the 55^th IEEE Conference on Decision and Control, Submitted, Las Vegas, 2016.