Darryl DeHaan

Extremum-seeking control of state-constrained nonlinear systems

Abstract This paper treats an extremum seeking control problem for a class of state-constrained nonlinear systems with unknown parameters. Using an interior-point approach, an adaptive method is proposed for generating set-points online which converge to the feasible extremum point of an objective function containing unknown parameters. A tracking controller ensures system states remain feasible at all times. A simulation example demonstrates application of the method.

A Real-time Framework for Model Predictive Control of Continuous-Time Nonlinear Systems

A new formulation of continuous-time nonlinear model predictive control (NMPC) is developed which accounts for dynamics associated with minimization of the optimal control problem. In doing so, it is shown that the stability of NMPC can be maintained for fast processes in which the computation time is significant with respect to the process dynamics. Our framework generalizes recent results for piecewise constant NMPC of continuous-time processes.

A new real-time method for nonlinear model predictive control

A formulation of continuous-time nonlinear MPC is proposed in which input trajectories are described by general time-varying parameterizations. The approach entails a limiting case of suboptimal single-shooting, in which the dynamics of the associated NLP are allowed to evolve within the same timescale as the process dynamics, resulting in a unique type of continuous-time dynamic state feedback which is proven to preserve stability and feasibility.

Adaptive robust MPC: An eye towards computational simplicity

Abstract This work addresses the challenging problem of constrained adaptive stabilization of a general nonlinear system involving affine parametric uncertainty. The approach is based upon a recently proposed methodology for unifying adaptive and model-predictive control, which involves the incorporation of set-valued adaptation into a robust-MPC framework. The contribution of this work is to demonstrate that this methodology is compatible with, and can improve upon the performance of, even the most simplistic tools for robust-MPC. This motivates the conclusion that any tradeoff between conservativeness and performance of the adaptive control can be achieved by appropriate selection of the underlying robust controller.

A NEW REAL-TIME APPROACH FOR NONLINEAR MODEL PREDICTIVE CONTROL

Abstract A new formulation of continuous-time nonlinear model predictive control is developed in which the parameters defining a piecewise-constant input trajectory are adapted continuously in real time. Stability is then proven when the parameter minimization evolves in the same timescale as the process dynamics. Pointwise constraints are incorporated by use of barrier functions.

Set-based estimation in discrete-time systems

This article presents new techniques for parameter identification for nonlinear dynamical discrete-time systems. The methods presented are intended to improve the performance of adaptive control systems such as RTO schemes and adaptive extremum-seeking systems. Using recent results on FT adaptive control, we develop alternative techniques that can be used to guarantee the convergence of parameter estimates to their true values in the presence of model-mismatch and exogenous variables. Three methods are presented. The first two methods rely on system excitation and a regressor matrix, in either case, the true parameters are identified when the regressor matrix is of full rank and can be inverted. The third method is based on a novel set-based adaptive estimation method proposed in Chapter 10 to simultaneously estimate the parameters and the uncertainty associated with the true value. The uncertainty set is updated periodically when sufficient information has been obtained to shrink the uncertainty set around the true parameters. Each method guarantees convergence of the parameter estimation error, provided an appropriate PE condition is met. The effectiveness of each method is demonstrated using a simulation example, displaying convergence of the parameter error estimation error.

Review of nonlinear MPC

The ultimate objective of a model predictive controller is to provide a closed-loop feedback that regulates to its target set in a fashion that is optimal with respect to the infinite-time problem, while enforcing pointwise constraints in a constructive manner.

Performance improvement in adaptive control

The FT identification method has two distinguishing features. First, the true parameter estimate is obtained at any time instant the excitation condition is satisfied, and second, the procedure allows for a direct and immediate removal of any perturbation signal injected into the closed-loop system to aid in parameter estimation. However, the drawback of the FT identification algorithm is the requirement to check the invertibility of a matrix online and compute the inverse matrix when appropriate. To avoid these concerns and enhance the applicability of the FT method in practical situations, the procedure is hereby exploited to develop a novel adaptive compensator that (almost) recovers the performance of the FTI. The compensator guarantees exponential convergence of the parameter estimation error at a rate dictated by the closed-loop systems excitation. It was shown how the adaptive compensator can be used to improve upon existing adaptive controllers. The modification proposed guarantees exponential stability of the parametric equilibrium provided the given PE condition is satisfied. Otherwise, the original systems closed-loop properties are preserved.

Robust adaptive economic MPC

In this chapter, we propose the design of economic MPC systems based on a singlestep approach of the adaptive MPC technique proposed for a class of uncertain nonlinear systems subject to parametric uncertainties and exogenous variables. The framework considered assumes that the economic function is a known function of constrained systems states, parameterized by unknown parameters. The objective and constraint functions may explicitly depend on time, which means that our proposed method is applicable to both dynamic and steady-state economic optimization. A simulation example is used to demonstrate the effectiveness of the design technique.

Extensions for performance improvement

In this book, we focus on the more typical role of adaptation as a means of coping with uncertainties in the system model. A standard implementation of MPC using a nominal model of the system dynamics can, with slight modification, exhibit nominal robustness to disturbances and modeling error. However in practical situations, the system model is only approximately known, so a guarantee of robustness which covers only “sufficiently small” errors may be unacceptable. In order to achieve a more solid robustness guarantee, it becomes necessary to account (either explicitly, or implicitly) for all possible trajectories which could be realized by the uncertain system, in order to guarantee feasible stability. The obvious numerical complexity of this task has resulted in an array of different control approaches, which lie at various locations on the spectrum between simple, conservative approximations versus complex, high-performance calculations. Ultimately, selecting an appropriate approach involves assessing, for the particular system in question, what is an acceptable balance between computational requirements and closed-loop performance.