Gene A. Bunin

Input Filter Design for Feasibility in Constraint-Adaptation Schemes

The subject of real-time, steady-state optimization under significant uncertainty is addressed in this paper. Specifically, the use of constraint-adaptation schemes is reviewed, and it is shown that, in general, such schemes cannot guarantee process feasibility over the relevant input space during the iterative process. This issue is addressed via the design of a feasibility-guaranteeing input filter, which is easily derived through the use of a Lipschitz bound on the plant behavior.While the proposed approach works to guarantee feasibility for the single-constraint case, early sub-optimal convergence is noted for cases with multiple constraints. In this latter scenario, some constraint violations must be accepted if convergence to the optimum is desired. An illustrative example is given to demonstrate these points.

Run-to-Run MPC Tuning via Gradient Descent

A gradient-descent method for the run-to-run tuning of MPC controllers is proposed. It is shown that, with an assumption on process repeatability, the MPC tuning parameters may be brought to a locally optimal set. SISO and MIMO examples illustrate the characteristics of the proposed approach.

Exploiting local quasiconvexity for gradient estimation in modifier-adaptation schemes

A new approach for gradient estimation in the context of real-time optimization under uncertainty is proposed in this paper. While this estimation problem is often a difficult one, it is shown that it can be simplified significantly if an assumption on the local quasiconvexity of the process is made and the resulting constraints on the gradient are exploited. To do this, the estimation problem is formulated as a constrained weighted least-squares problem with appropriate choice of the weights. Two numerical examples illustrate the effectiveness of the proposed method in converging to the true process optimum, even in the case of significant measurement noise.

Iterative Controller Tuning by Real-Time Optimization

The present article looks at the problem of iterative controller tuning, where the parameters of a given controller are adapted in an iterative manner to bring the user-defined performance metric to a local minimum for some repetitive process. Specifically, we cast the controller tuning problem as a real-time optimization (RTO) problem, which allows us to exploit the available RTO theory to enforce both convergence and performance guarantees. We verify the effectiveness of the proposed methodology on an experimental torsional system and note that the results are particularly promising considering the simplicity of the method.

Extended reverse-convex programming: an approximate enumeration approach to global optimization

A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many branch-and-bound methods, the proposed approach approximates the NLP problem by a reverse-convex programming (RCP) problem to a controlled precision, with the latter then solved by an enumerative search. To establish the theoretical guarantees of the method, the notion of “RCP regularity” is introduced and it is proven that enumeration is guaranteed to yield a global optimum when the RCP problem is regular. An extended RCP algorithmic framework is then presented and its performance is examined for a small set of test problems.