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Integrating nonlinear control tools with optimization-based control approaches

Industrial process control systems need to be designed to explicitly deal with limitations (constraints) in the capacity of the control actuators and to satisfy bounds on the evolution of the process state variables to prevent severe deterioration in the nominal closed-loop performance and even lead to closed-loop instability. In current industrial practice, the achievement of high performance, under control and state constraints, relies to a large extent on the use of model predictive control (MPC) policies. However, the ability of the available model predictive controllers to guarantee closed-loop stability and enforce constraint satisfaction is dependent on the assumption of feasibility (i.e., existence of a solution) of the constrained optimization problem. This limitation strongly impacts the practical implementation of the model predictive control policies and limits the a priori (i.e., before controller implementation) characterization of the set of initial conditions, starting from where the constrained optimization problem is feasible and closed-loop stability is guaranteed.

One direction of investigation is the design of nonlinear predictive controllers that not just enhance, but stabilize nonlinear systems (or at least a large class of nonlinear systems) from the entire set of initial conditions from where stabilization is achievable. Another possibility is to combine the proposed predictive controllers with observers for nonlinear systems that account for uncertainty and process noise, and yet provide convergence guarantees.

Dr. Prashant Mhaskar
Professor and Canada Research Chair in Nonlinear and Fault-Tolerant Control
Lyapunov-Based Offset-free Model Predictive Control of Nonlinear Process Systems
Can J Chem Eng, 93 (3) 471-478 (2015)  -  [ Publisher Version ]
Offset-free Model Predictive Control of a Heat Pump
Wallace, M., House, J, Salisbury, T, Mhaskar, P.
Ind Eng Chem Res, 54 (3) 994-1005 (2015)  -  [ Publisher Version ]
Offset-free Model Predictive Control of a Heat Pump
Proceedings of the American Control Conference, 2247 - 2252 (2014)  -  [ Publisher Version ]
Lyapunov-based Offset-Free Model Predictive Control of Nonlinear Systems
Proceedings of the American Control Conference, 2839-2844 (2014)  -  [ Publisher Version ]
Predictive Control Methods to Improve Energy Efficiency and Reduce Demand in Buildings
Salsbury, Timothy, Mhaskar, P., Qin, S Joe
Comp Chem Eng, 51 77-85 (2013)  -  [ Publisher Version ]
Offset-Free Model Predictive Control Of A VCC
Wallace, M.Das, B.Mhaskar, P., Salsbury, T., House, J.
J Proc Contr, 22 1374-1386 (2012)  -  [ Publisher Version ]