Robust Constrained Model Predictive Control using Linear Matrix Inequalities

The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a state-feedback control law which minimizes a "worst-case" infinite horizon objective function, subject to constraints on the control input and plant output. Using standard techniques, the problem of minimizing an upper bound on the "worst-case" objective function, subject to input and output constraints, is reduced to a convex optimization involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon state-feedback control design robustly stabilizes the set of uncertain plants under consideration. Several extensions, such as application to systems with time-delays and problems involving constant set-point tracking, trajectory tracking and disturbance rejection, which follow naturally from our formulation, are discussed. The controller design procedure is illustrated with two examples. Finally, conclusions are presented

Adaptive model predictive control

The problem of model predictive control (MPC) under parametric uncertainties for a class of nonlinear systems is addressed. An adaptive identi er is used to estimate the pa- rameters and the state variables simultaneously. The algorithm proposed guarantees the convergence of parameters and the state variables to their true value. The task is posed as an adaptive model predictive control problem in which the controller is required to steer the system to the system setpoint that optimizes a user-speci ed objective function. The technique of adaptive model predictive control is developed for two broad classes of systems. The rst class of system considered is a class of uncertain nonlinear systems with input to state stability property. Using a generalization of the set-based adaptive estimation technique, the estimates of the parameters and state are updated to guarantee convergence to a neighborhood of their true value. The second involves a method of determining appropriate excitation conditions for nonlin- ear systems. Since the identi cation of the true cost surface is paramount to the success of the integration scheme, novel parameter estimation techniques with better convergence properties are developed. The estimation routine allows exact reconstruction of the systems unknown parameters in nite-time. The applicability of the identi er to improve upon the performance of existing adaptive controllers is demonstrated. Then, an adaptive nonlinear model predictive controller strategy is integrated to this estimation algorithm in which ro- bustness features are incorporated to account for the e ect of the model uncertainty. To study the practical applicability of the developed method, the estimation of state vari- ables and unknown parameters in a stirred tank process has been performed. The results of the experimental application demonstrate the ability of the proposed techniques to estimate the state variables and parameters of an uncertain practical system.Departamento de Ingeniería de Sistemas y AutomáticaMáster en Investigación en Ingeniería de Procesos y Sistemas Industriale

A data-driven model inversion approach to cancer immunotherapy control

A novel data-driven control design approach for Multiple Input Multiple Output nonlinear systems is proposed in the paper, relying on the identification of a polynomial prediction model of the system to control and its on-line inversion. A simulated study is then presented, concerning the design of a control strategy for cancer immunotherapy. This study shows that the proposed approach may be quite effective in treating cancer patients, and may give results similar to (or perhaps better than) those provided by “standard” methods. The fundamental difference is that “standard” methods are typically based on the unrealistic assumption that an accurate physiological model of the cancer-immune mechanism is avail- able; in the approach proposed here, the controller is designed without such a strong assumption

Optimal Ventilation Control in Complex Urban Tunnels with Multi-Point Pollutant Discharge

We propose an optimal ventilation control model for complex urban vehicular tunnels with distributed pollutant discharge points. The control problem is formulated as a nonlinear integer program that aims to minimize ventilation energy cost while meeting multiple air quality control requirements inside the tunnel and at discharge points. Based on the steady-state solutions to tunnel aerodynamics equations, we propose a reduced form model for air velocities as explicit functions of ventilation decision variables and traffic density. A compact parameterization of this model helps to show that tunnel airflows can be estimated using standard linear regression techniques. The steady-state pollutant dispersion model is then incorporated for the derivation of optimal pollutant discharge control strategies. A case study of a new urban tunnel in Hangzhou, China demonstrates that the scheduling of fan operations based on the proposed optimization model can effectively achieve different air quality control objectives under varying traffic intensity.U.S. Department of Transportation 69A355174711

Observer-Based Adaptive Control

The work present in this master thesis relates to output feedback adaptive control and observer design of nonlinear systems, and in particular of robot manipulators. A continuous-time velocity observer and a discrete-time adaptive velocity observer for robots are shown, and an observer backstepping controller is also proposed, which can be used together with both the observers. The resulting closed-loop system is proven to be semiglobally asymptotically stable with respect to both the velocity observation error and the tracking error, and stable with respect to the parameter estimation error. Furthermore an on-line parameter estimation method for a class of nonlinear system is presented, which can be easily extended for the robot equation. Unfortunately the way to use it in combination with the previous observer-controller has not been found and it has not been used in the experiments. In the Appendix A some technical details about the al-gorithm implementation are included, and in the Appendix B a paper already submitted to the 2002 Conference in Decision and Control is included, in which the adaptive output-feedback control scheme is extended for ship control. All the work has been conducted in the Department of Automatic Control, Lund Institute of Technology, Lund University

Feedback Linearizing Control Strategies for Chemical Engineering Applications.

Two widely studied control techniques which compensate for process nonlinearities are feedback linearization (FBL) and nonlinear model predictive control (NMPC). Feedback linearization has a low computational requirement but provides no means to explicitly handle constraints which are important in the chemical process industry. Nonlinear model predictive control provides explicit constraint compensation but only at the expense of high computational requirements. Both techniques suffer from the need for full-state feedback and may have high sensitivities to disturbances. The main work of this dissertation is to eliminate some of the disadvantages associated with FBL techniques. The computation time associated with solving a nonlinear programming problem at each time step restricts the use of NMPC to low-dimensional systems. By using linear model predictive control on top of a FBL controller, it is found that explicit constraint compensation can be provided without large computational requirements. The main difficulty is the required constraint mapping. This strategy is applied to a polymerization reactor, and stability results for discrete-time nonlinear systems are established. To alleviate the need for full-state feedback in FBL techniques it is necessary to construct an observer, which is very difficult for general nonlinear systems. A class of nonlinear systems is studied for which the observer construction is quite easy in that the design mimics the linear case. The class of systems referred to are those in which the unmeasured variables appear in an affine manner. The same observer construction can be used to estimate unmeasured disturbances, thereby providing a reduction in the controller sensitivity to those disturbances. Another contribution of this work is the application of feedback linearization techniques to two novel biotechnological processes. The first is a mixed-culture bioreactor in which coexistence steady states of the two cell populations must be stabilized. These steady states are unstable in the open-loop system since each population competes for the same substrate, and each has a different growth rate. The requirement of a pulsatile manipulated input complicates the controller design. The second process is a bioreactor described by a distributed parameter model in which undesired oscillations must be damped without the use of distributed control

Applied Nonlinear Control of Unmanned Vehicles with Uncertain Dynamics

The presented research concerns the control of unmanned vehicles. The results introduced in this dissertation provide a solid control framework for a wide class of nonlinear uncertain systems, with a special emphasis on issues related to implementation, such as control input amplitude and rate saturation, or partial state measurements availability. More specifically, an adaptive control framework, allowing to enforce amplitude and rate saturation of the command, is developed. The motion control component of this framework, which works in conjunction with a saturation algorithm, is then specialized to different types of vehicles. Vertical take-off and landing aerial vehicles and a general class of autonomous marine ve-hicles are considered. A nonlinear control algorithm addressing the tracking problem for a class of underactuated, non-minimum phase marine vehicles is then introduced. This motion controller is extended, using direct and indirect adaptive techniques, to handle parametric uncertainties in the system model. Numerical simulations are used to illustrate the efficacy of the algorithms. Next, the output feedback control problem is treated, for a large class of nonlinear and uncertain systems. The proposed solution relies on a novel nonlinear observe