An MPC Approach to Dual Control

Abstract We present a model predictive control (MPC) approach to solve the dual adaptive control problem. The cost function minimized by the controller rewards probing the system for information when the parameter estimates are poor. The control algorithm is designed to handle poorly identified models and excites the system so that information can be gathered to achieve the optimal trade-off between process control and identification. This excitation is achieved without requiring the input to be persistently exciting; rather, the probing objective is based on an exact formulation of the expected value of the output error at the first time stage. The resulting expression is also used for the second time stage; this ensures that a proper trade-off between excitation and output regulation is maintained. The algorithm can be viewed as the merging of adaptive control with MPC and its design can easily be implemented with modifications to an existing MPC. As an example we consider a first-order linear process system with two unknown parameters. Our proposed algorithm probes the system even when the output error is small and quickly gathers enough information to correctly identify the unknown plant parameters.

[1]  K. Åström,et al.  Dual Control of an Integrator with Unknown Gain , 1986 .

[2]  Steven Clark,et al.  General Algebraic Modeling System , 2014 .

[3]  Bengt Mårtensson,et al.  The order of any stabilizing regulator is sufficient a priori information for adaptive stabilization , 1985 .

[4]  H. Genceli,et al.  New approach to constrained predictive control with simultaneous model identification , 1996 .

[5]  Bjarne Foss,et al.  An Adaptive Model Predictive Dual Controller , 2013, ALCOSP.

[6]  Michel Gevers.  A decade of progress in iterative process control design: from theory to practice , 2002 .

[7]  Tamer Basar,et al.  Dual Control Theory , 2001 .

[8]  Richard M. Johnstone,et al.  Exponential convergence of recursive least squares with exponential forgetting factor , 1982, 1982 21st IEEE Conference on Decision and Control.

[9]  Bjarne A. Foss,et al.  Towards Dual MPC , 2012 .

[10]  Alan Schumitzky,et al.  Implicit dual control based on particle filtering and forward dynamic programming , 2008, International journal of adaptive control and signal processing.

[11]  Jong Min Lee,et al.  An approximate dynamic programming based approach to dual adaptive control , 2009 .

[12]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[13]  M. Radenković,et al.  Using Persistent Excitation with Fixed Energy to Stabilize Adaptive Controllers and Obtain Hard Bounds for the Parameter Estimation Error , 1993, 1993 American Control Conference.

[14]  M. Radenković,et al.  Using Persistent Excitation with Fixed Energy to Stabilize AdaptiveControllers and Obtain Hard Bounds for the Parameter Estimation Error , 1995 .

[15]  Robert R. Bitmead,et al.  Persistently Exciting Model Predictive Control for SISO systems , 2012 .

[16]  L. Biegler,et al.  A reduced space interior point strategy for optimization of differential algebraic systems , 2000 .

[17]  Michael Nikolaou,et al.  Effect of on-line optimization techniques on model predictive control and identification (MPCI) , 2002 .