Predictive neuro-control of uncertain systems: design and use of a neuro-optimizer

We consider the problem of predictive control of uncertain stochastic discrete I/O systems. Given a model identification procedure able to give accurate output system estimates, e.g. a neural network approximation, we use another feedforward neural network to generate at each time step a constrained optimal control. Dynamic backpropagation is used to improve when necessary the controller network parameters. Both system and controller neural structures are first selected off-line by a statistical Bayesian procedure in order to make the predictive control minimizing process more efficient. The issue of stochastic stability of the closed-loop is considered. We developed this approach for the tracking control of such uncertain systems as biotechnological processes. Actual and simulated predictive neuro-control case studies in this field of application are proposed as illustrations. A comparison with a more classic quasi-Newton-based approach is also proposed, showing the interest of this neuro-control approach.     

New design relations for 2-DOF PID-like control systems

Self-regulating processes can be controlled by internal model control systems where the usual three-parameter model of the process is transformed into a rational model via a parametrized first-order approximant of the apparent dead time. Using feedback and feedforward compensators leads to 2-DOF PID controllers whose time constants cancel that of the rational model. To obtain the desired sensitivity of the actual control loop, the model adaptation parameter and a gain tuning factor in the control system are determined by functions of the normalized dead time. The response to setpoint changes is selected by means of the feedforward compensator or via a prefilter. Plots of the sensitivity and the simulation of step responses to changes in the controller setpoint or to disturbances, show the validity of these design relations for transfer functions representative of typical industrial processes.     

Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function

In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed using a saturation-dependent Lyapunov function. This saturation-dependent Lyapunov function captures the real-time information on the severity of actuator saturation and leads to less conservative estimate of the domain of attraction, which is based on the solution of an LMI optimization problem. Numerical examples are presented to show the effectiveness of the proposed method.     

A new separation result for a class of quadratic-like systems with application to Euler-Lagrange models

A separation result for some kind of global stabilization via output feedback of a class of nonlinear systems, under the form of some stabilizability by state feedback on the one hand, and some unboundedness observability on the other hand is presented. They allow to design, for any domain of output initial condition, some dynamic output feedback controller achieving global stability. It is also highlighted how disturbance attenuation can further be achieved on the same basis. As an example, the proposed conditions are shown to be satisfied by the class of so-called Euler-Lagrange systems, for which a tracking output feedback control law is thus proposed.     

Unknown disturbance inputs estimation based on a state functional observer design

We consider the problem of function of state plus unknown input estimation of a linear time-invariant system using only the measured outputs. Two reduced-order input estimators built upon a state functional observer are proposed. The first is an extension of a state/input estimator, while the second is based on adaptive observer design technique. The proposed estimator can be designed under less restrictive conditions than those of the previous work, and unlike some of the past studies the proposed observer can be designed for certain nonminimum phase systems.     

On the H fixed-lag smoothing: how to exploit the information preview

The problem of the continuous-time H^∞ fixed-lag smoothing over the infinite horizon is studied. The first solution to the problem is derived in terms of one algebraic Riccati equation of the same dimension as in the filtering case and the mechanism by which the performance improvements with respect to the H^∞ filtering occur is clarified. It is shown that the H^∞ smoother exploits the information preview in an “H² manner”.     

The periodic optimality of LQ controllers satisfying strong stabilization

An LQ strong stabilization problem is proposed. To determine when a controller with periodic gains is locally superior to a linear time invariant compensator for this problem, a Π test is presented. For systems with strictly proper transfer functions, it is proven that the frequency range where stable periodic controllers based on weak variations about the LTI case can give better performance than stable LTI compensators is finite. In the development, a means to evaluate the second partials of functions with respect to matrix-valued parameters is introduced. For those systems where periodic control is warranted, techniques for designing optimal periodic strongly stabilizing controllers are presented. Two examples detailing the application of the Π test are provided, as well as an optimal periodic controller design example.     

Recursive algorithms for inner ellipsoidal approximation of convex polytopes

In this paper, fast recursive algorithms for the approximation of an n-dimensional convex polytope by means of an inscribed ellipsoid are presented. These algorithms consider at each step a single inequality describing the polytope and, under mild assumptions, they are guaranteed to converge in a finite number of steps. For their recursive nature, the proposed algorithms are better suited to treat a quite large number of constraints than standard off-line solutions, and have their natural application to problems where the set of constraints is iteratively updated, as on-line estimation problems, nonlinear convex optimization procedures and set membership identification.     

A convex parametrization of risk-adjusted stabilizing controllers

The focal point of this paper is the synthesis of controllers under risk-specifications. In recent years there has been a growing interest in the development of techniques for controller design where, instead of requiring that the performance specifications are met for every possible value of admissible uncertainty, it is required that the risk of performance violation is below a small well-defined risk level. In contrast to previous work, where the search for the controller gains is done using randomized algorithms, the results in this paper show that for a class of uncertain linear time invariant systems, the search for the “risk-adjusted” controller can be done efficiently using deterministic algorithms. More precisely, for the case when the characteristic polynomial of the closed loop system depends affinely on the uncertainty, we provide a convex parametrization of “risk-adjusted” stabilizing controllers.     

A random least-trimmed-squares identification algorithm

The Least-trimmed-squares (LTS) estimator is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. In this paper, we propose a random LTS algorithm which has a low computational complexity that can be calculated a priori as a function of the required error bound and the confidence interval. Moreover, if the number of data points goes to infinite, the algorithm becomes a deterministic one that converges to the true LTS in some probability sense.