Model Predictive Control: Multivariable Control Technique of Choice in the 1990s?

The state space and input/output formulations of model predictive control are compared and preference is given to the former because of the industrial interest in multivariable constrained problems. Recently, by abandoning the assumption of a finite output horizon several researchers have derived powerful stability results for linear and nonlinear systems with and without constraints, for the nominal case and in the presence of model uncertainty. Some of these results are reviewed. Optimistic speculations about the future of MPC conclude the paper

EXPERIENCE OF ROMANIA IN THE ELABORATION AND IMPLEMENTATION OF THE DOMESTIC POLICIES OF EUROPEAN INTEGRATION: LESSONS FOR THE REPUBLIC OF MOLDOVA

This article represents an analysis of the experience of Romania in accession and integration of the state into the European Union. It is a tentative to identify Romanian domestic policies of European integration. In order to achieve this objective, the study is focused on analyzing the evolution of Romania accession negotiations, internal and external activities and problems of country’s European integration. Another important goal of the article was to identify some important conclusions for the European roadmap of the Republic of Moldova under the experience of Romania. The main lesson for the Republic of Moldova presented by the author is that for a successful European integration of the Republic of Moldova it is essential to prepare the country from inside by formulating and providing in practice concrete tasks and mechanisms in the internal policies of the country.European integration, internal policies, experience, accession, negotiations, lessons

Stability of Model Predictive Control with Soft Constraints

We derive stability conditions for Model Predictive Control (MPC) with hard constraints on the inputs and "soft" constraints on the outputs for an infinitely long output horizon. We show that with state feedback MPC is globally asymptotically stabilizing if and only if all the eigenvalues of the open loop system are in the closed unit disk. With output feedback the eigenvalues must be strictly inside the unit circle. The on-line optimization problem defining MPC can be posed as a finite dimensional quadratic program even though the output constraints are specified over an infinite horizon

Minimizing the Euclidean Condition Number

This paper considers the problem of determining the row and/or column scaling of a matrix A that minimizes the condition number of the scaled matrix. This problem has been studied by many authors. For the cases of the ∞-norm and the 1-norm, the scaling problem was completely solved in the 1960s. It is the Euclidean norm case that has widespread application in robust control analyses. For example, it is used for integral controllability tests based on steady-state information, for the selection of sensors and actuators based on dynamic information, and for studying the sensitivity of stability to uncertainty in control systems. Minimizing the scaled Euclidean condition number has been an open question—researchers proposed approaches to solving the problem numerically, but none of the proposed numerical approaches guaranteed convergence to the true minimum. This paper provides a convex optimization procedure to determine the scalings that minimize the Euclidean condition number. This optimization can be solved in polynomial-time with off-the-shelf software

Estimation of Cross Directional Properties: Scanning versus Stationary Sensors

Periodic time varying Kalman filter calculations for problems involving scanning sensors are solved using "lifting" techniques common for multirate systems. The solution of this problem is used to compare the performance of scanning sensors versus stationary sensors in the estimation of cross directional properties. Furthermore, we examine controller performance when the outputs from the Kalman filter are used as inputs to a state feedback control law. Although adding sensors may significantly enhance the estimates of cross directional properties, feedback of these improved estimates may translate to lower levels of improvement in cross directional variations

Performance Monitoring of Control Systems using Likelihood Methods

Evaluating deterioration in performance of control systems using closed loop operating data is addressed. A framework is proposed in which acceptable performance is expressed as constraints on the closed loop transfer function impulse response coefficients. Using likelihood methods, a hypothesis test is outlined to determine if control deterioration has occurred. The method is applied to a simulation example as well as data from an operational distillation column, and the results are compared to those obtained using minimum variance estimation approaches

Stability and Performance Analysis of Systems Under Constraints

All real world control systems must deal with actuator and state constraints. Standard conic sector bounded nonlinearity stability theory provides methods for analyzing the stability and performance of systems under constraints, but it is well-known that these conditions can be very conservative. A method is developed to reduce conservatism in the analysis of constraints by representing them as nonlinear real parametric uncertainty

Optimal and Robust Design of Integrated Control and Diagnostic Modules

The problem of designing an integrated control and diagnostic module is considered. The four degree of freedom controller is recast into a general framework wherein results from optimal and robust control theory can be easily implemented. For the case of an H2 objective, it is shown that the optimal control-diagnostic module involves constructing an optimal controller, closing the loop with this controller, and then designing an optimal diagnostic module for the closed loop. When uncertain plants are involved, this two-step method does not lead to reasonable diagnostics, and the control and diagnostic modules must be synthesized simultaneously. An example shows how this design can be accomplished with available methods

Significance Regression: Robust Regression for Collinear Data

This paper examines robust linear multivariable regression from collinear data. A brief review of M-estimators discusses the strengths of this approach for tolerating outliers and/or perturbations in the error distributions. The review reveals that M-estimation may be unreliable if the data exhibit collinearity. Next, significance regression (SR) is discussed. SR is a successful method for treating collinearity but is not robust. A new significance regression algorithm for the weighted-least-squares error criterion (SR-WLS) is developed. Using the weights computed via M-estimation with the SR-WLS algorithm yields an effective method that robustly mollifies collinearity problems. Numerical examples illustrate the main points