Abstract
Model predictive control and identification (MPCI) is a new class of adaptive controllers, that employ the following on-line optimization to perform closed-loop identification and controller adaptation : at each time step minimize an objective function subject to (a) standard MPC constraints and (b) persistent excitation constraints on the process inputs . While the MPCI formulation may carry a standard control objective, it provides wide flexibility for defining different objectives as well. In this work we propose a new variant of MPCI. In this variant, the on-line objective is not to minimize the sum of square errors, but to maximize the sum of the lower bounds on the minimum eigenvalues of the information matrices over a finite horizon. In that way, inputs to the process are allowed to excite the process highly enough to generate as much modeling information as possible, while the process goes off-spec as little as possible. In MPCI variant the control objective is achieved with output constraints, which can be loosened or tightened with the need of identification. The resulting on-line optimization problem requires, at each time step, the solution of a semidefinite program, with nonconvex quadratic matrix inequalities. To obtain a guaranteed local optimum, we first linearize each quadratic matrix inequality to get a linear matrix inequality (LMI) which can then be used in standard semidefinite programming codes to find a suboptimal point. The quadratic matrix inequalities are then linearized again at this suboptimal point and the resulting semidefinite program is solved. This process is repeated until a convergence criterion is met.
Eker, Sukru Alper (1998). MPCI: the capabilities of closed loop process identification by establishing a new paradigm. Master's thesis, Texas A&M University. Available electronically from
https : / /hdl .handle .net /1969 .1 /ETD -TAMU -1998 -THESIS -E354.