Date of final exam: 07/03/2000

E-mail: angeli@dsi.unifi.it

Tutor: Prof.  E. Mosca, Università di Firenze

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Control strategies for systems under constraints   ___________________________________________________________________________________________________________

Advisor:

Prof.  E. Mosca, Università di Firenze

Summary of the thesis

The study of systems under constraints is an extremely relevant issue in automatic control. It is not an overstatement saying that virtually all systems are subject to constraints of some nature when looked at from the automatic control point of view. We usually distinguish between input constraints and state constraints. This distinction, appealing from a physical point of view, it is to a certain extent also reflected in the mathematical tools needed in order to take care of them. Input constraints usually arise due to actuators limitations. In classical control theory, actuators are modeled as linear systems. This approximation is only suitable if it is a priori known that the control effort be small compared to the effective capabilities of the real actuator. As a matter of fact, the risk of a design process carried out without explicitly taking into account actuators saturations in very high. The least we can expect is a sharp decay of the preformances; in other cases the delay and phase-lag introduced by the nonlinearity can even affect the plant stability. State constraints are often related to limitations of the plant itself. For instance a robot arm could operate in a partially obstructed environment so that its degrees of freedom would be limited or safety prescriptions might impose limitations on speeds or tensions during the operations. Among the different approaches for the study of control systems we decided in this thesis to develop a couple of methods which borrow some ideas from predictive control. In particular the receding horizon approach is the common line throughout the discussed algorithms. Two variants are considered, one for input constraints (plus, optionally, input increments) and the other for state constraints. In particular, in the first scheme predictive control is used in order to enhance the performances of a gain-scheduling controller which achieves stability of a plant through switching between linear low-gain feedback laws. In the literature in fact, the problem of stability of linear systems subject to input constraints was tackled several times, but the performance aspect has often been disregarded. The second scheme is a reduced-complexity controller. The only degrees of freedom are in the virtual reference (rather than in the virtual command as it happens in classic MPC), which is filtered on-line in order to ensure contraints fulfillment. This device, which does not take care of stabilizing the plant but is added in feedback to the plant as an additional control loop, is usually referred to as Reference Governor.

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OTHER RESEARCH TOPICS

External stability of nonlinear systems

Supervisor: Prof. E. Sontag, Rutger University

Unlike linear systems, where relationships between internal and external stability are well understood, the picture appears much more complex when considering nonlinear ones. Recently, the notions of input-to-state stability, introduced by Prof. Sontag, have proven to be a very interesting tool, both from a theoretical and practical point of view, in order to tackle in a systematic way problems of external stability for finite dimensional nonlinear systems evolving in euclidean space. In particular we studied the so called integral Input-to-State stability, which is a stability notion providin estimates of a state norm in terms of a transient due to initial conditions plus a second contribution due to the input energy of the system.
 

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