Stabilization and passification of uncertain systems via static output feedback

Control of systems with time-varying dynamical characteristics impose either a conservative time-invariant control strategy that should hold for all time instants or to adopt some adaptive scheme. One of such, called simple adaptive control, is particularly appropriate for control applications such as flexible aircrafts or other fast varying processes. Indeed, it does not need any real-time estimation of time-vaying parameters but adapts based on the unique sensors measurements. Yet, this control strategy, also called passivity-based adaptive control, needs to be applied for the system to be passifiable. Or at least it needs to exhibit a linear combination of the inputs and outputs such that this property holds. The paper is devoted to the search of such linear combinations with practical efficient algorithms. Results are discussed in detail for an uncertain time-varying aircraft control example

Stability analysis of 2D Roesser systems via vector Lyapunov functions

The paper gives new results that contribute to the development of a stability theory for 2D nonlinear discrete and differential systems described by a state-space model of the Roesser form using an extension of Lyapunov’s method. One of the main difficulties in using such an approach is that the full derivative or its discrete counterpart along the trajectories cannot be obtained without explicitly finding the solution of the system under consideration. This has led to the use of a vector Lyapunov function and its divergence or its discrete counterpart along the system trajectories. Using this approach, new conditions for asymptotic stability are derived in terms of the properties of two vector Lyapunov functions. The properties of asymptotic stability in the horizontal and vertical dynamics, respectively, are introduced and analyzed. This new properties arise naturally for repetitive processes where one of the two independent variables is defined over a finite interval. Sufficient conditions for exponential stability in terms of the properties of one vector Lyapunov function are also given as a natural follow on from the asymptotic stability analysis

Iterative learning control design for discrete stochastic linear systems

This paper develops a new iterative learning control law for stochastic linear systems. The design is based on recently developed passivity based control of repetitive process, which are a class 2D nonlinear systems. In particular, this theory is used to design a nonlinear control law for linear dynamics, which allows tuning of the control law to achieve better performance. A supporting example is given, including a comparison with a previously reported design.</p

Iterative Learning Control of Discrete Systems with Actuator Backlash using a Weighted Sum of Previous Trial Control Signals

This paper considers iterative learning control design for discrete dynamics in the presence of backlash in the actuators. A new control design for this problem is developed based on the stability theory for nonlinear repetitive processes. An example of this design's effectiveness is where the dynamics model was obtained using data collected from frequency response tests on a physical system

Iterative learning control of stochastic linear systems with reference trajectory switching

A reference trajectory is specified for systems that repetitively execute the same finite duration task in iterative learning control. In many current designs, the reference signal remains the same, but in others, it is desirable to allow the reference trajectory to change during the system’s overall operation. This paper develops a control law design method for linear dynamics where the measured signals are noise corrupted, random disturbances are present, and the reference trajectory is allowed to change during operation. The new design is based on the recently developed stochastic stability theory for repetitive processes, a class of 2D systems, and uses vector Lyapunov functions and their divergence properties. It also shows how to eliminate the transient error that results from a switch of the reference trajectory. A numerical case study demonstrates the applicability of the new design

Stabilization of two-dimensional nonlinear systems described by Fornasini-Marchesini and Roesser models

The paper considers nonlinear two-dimensional systems described by the Fornasini-Marchesini or Roesser state-space models. Conditions for such systems to have a physically motivated exponential stability property are derived using vector Lyapunov functions. A form of passivity, termed exponential passivity, is introduced and used, together with a vector storage function, to develop a feedback based control law that guarantees exponential stability of the controlled system. For cases where noise is present, stochastic dissipativity in the second moment is defined and then a particular case of this property, termed passivity in the mean square, is used, together with a vector storage function, to develop a feedback based control law such that the controlled system also has this property. Two physically motivated particular cases, a system with nonlinear actuator dynamics and additive noise and a linear system with state-dependent noise, respectively, are also considered to demonstrate the effectiveness of the new results.</p

Passivity based stabilization of repetitive processes and iterative learning control design

Repetitive processes are a class of 2D systems that arise in the modeling of physical systems and also as a setting for iterative learning control design. For linear dynamics experimental validation of iterative learning control laws designed in this setting has been successfully achieved. Examples also exist where a linear model is not sufficient for analysis and control law design. This has led to research on the development of a stability and control law design theory for nonlinear repetitive processes. In this paper new results on a passivity based approach to control law design for these processes are developed. These results are then extended to iterative learning control, resulting in a design where tuning of the control law to achieve better performance is possible.</p