Javier Ruiz-León

Observability of Switched Linear Systems

This work deals with finite time observability of switched linear systems (SLS) when they are represented by a family of nonautonomous linear systems (LS) and an interpreted Petri net (IPN). Based on this SLS representation, new detection of the commutation time and LS distinguishability characterizations in SLS extended to the non autonomous case are presented. Using these results, the novel concept of distinguishability between LS sequences is presented and characterized. This concept together with the IPN input-output information is used to determine the IPN marking sequence. From the knowledge of this sequence, the conditions for the computation of the continuous state are presented. Also necessary and sufficient conditions for the observability in infinitesimal time are provided.

Singular perturbation based solution to optimal microalgal growth problem and its infinite time horizon analysis

The problem of the optimal microalgal growth is considered here. The objective is to maximize the specific growth rate of microalgae by manipulating the irradiance. The model describing the growth of microalgae is based on the mechanistic description in the form of the so called photosynthetic factory (PSF) resulting into the second order bilinear system which is, nevertheless, known in biotechnological literature to comprise many important features of microalgal growth. To obtain the solution of optimal control problem, the singular perturbation approach is used here to reduce fast components of system dynamics leading to a less dimensional system with more complex performance index which allows a nice analytical solution. Its infinite horizon analysis shows that the optimal solution on large time intervals tends to the optimal steady state of PSF thereby supporting the hypothesis often mentioned in the biotechnological literature. Finally, the numerical algorithm to compute optimal control is applied to the original non-reduced system giving very similar results as the reduction based approach.

Greenhouse Modeling Using Continuous Timed Petri Nets

This paper presents a continuous timed Petri nets (ContPNs) based greenhouse modeling methodology. The presented methodology is based on the definition of elementary ContPN modules which are designed to capture the components of a general energy and mass balance differential equation, like parts that are reducing or increasing variables, such as heat, CO2 concentration, and humidity. The semantics of ContPN is also extended in order to deal with variables depending on external greenhouse variables, such as solar radiation. Each external variable is represented by a place whose marking depends on an a priori known function, for instance, the solar radiation function of the greenhouse site, which can be obtained statistically. The modeling methodology is illustrated with a greenhouse modeling example.

ABS + active suspension control via sliding mode and linear geometric methods for disturbance attenuation

This paper deals with the control of an Anti-lock Brake System (ABS) assisted with an active suspension. The main objective is to track the slip rate of a car and ensure a shorter distance in the braking process. For the ABS subsystem an integral nested sliding mode controller based on the block control principle is designed. On the other hand, for the active suspension subsystem a sliding mode controller based on regular form and linear geometric techniques is proposed. Both closed-loop subsystems are robust in presence of matched and unmatched perturbations. To show the performance of the proposed control strategy, a simulation study is carried on, where results show good behavior of the ABS with active suspension under variations in the road.

Formation and trajectory tracking of a class of nonlinear systems with super twisting control

This work proposes a decentralized super twisting control scheme for group formation and trajectory tracking of multi-agent system networks with a fixed topology. Each agent dynamics is represented by a single-input single-output nonlinear system in its normal form and the information required by each controller is the output of the others agents. It is proved that output consensus and trajectory tracking can be achieved with the proposed super twisting control. Moreover, the state space representation of the agents dynamics is not restricted to be of the same dimension, as usually assumed in the literature. The stability of the controlled system is proved using a Lyapunov function and a simulation example is provided in order to illustrate the application of the proposed control.

Sliding mode observer for Switched Linear Systems

This work is concerned with the design of an observer for Switched Linear Systems (SLS) subject to an unknown switching signal. The convergence of the proposed SLS observer is proved, based on observability results for SLS, for the following two cases. First, it is shown that if the discrete state of the SLS is observable, then the observer estimates the switching signal, even though the individual Linear System (LS) may not be observable. And second, it is shown how the observer may provide an estimate of the continuous variables, even though the discrete state is unknown.

Real-Time Error-Feedback Output Regulation of Nonhyperbolically Nonminimum Phase System

A real time implementation of an error feedback output regulation problem for the gyroscopical platform is presented here. It is based on a numerical method for the solution of the so-called regulator equation. The regulator equation consists of partial differential equations combined with algebraic ones and arises when solving the output-regulation problem. Error-feedback output regulation problem aims to find a dynamic feedback compensator using only tracking error measurements to ensure tracking given reference and/or rejecting unknown disturbance. Solving the regulator equation is becoming difficult especially for the non-minimum phase systems where reducing variables against algebraic part leads to possible unsolvable differential part. The proposed numerical method is based on the successive approximation of the differential part of the regulator equation by the finite-element method while trying to minimize functional expressing the error of its algebraical part. This solution is then used to design real-time controller which is successfully experimentally tested.

Formation and trajectory tracking of discrete-time multi-agent systems using block control

The design of a decentralized discrete-time block control scheme, for a multi-agent system with a fixed topology, to achieve formation and trajectory tracking is proposed in this work. Each agent dynamics is represented either by a first-order or second-order discrete-time system, only the position of each agents neighbors is measured and their velocity and acceleration are unknown, and exclusively the agents that are connected to the virtual agent have full information of the reference. Each agent is provided with discrete-time state observers for the velocity and acceleration of its neighbors. It is proved that formation and trajectory tracking can be achieved applying the proposed block control with a consensus scheme. The stability of the controlled system with the state observer is proved.

A distributed control design for the output regulation and output consensus of a class of switched linear multi-agent systems

This paper presents the design of a distributed control law for output regulation and output consensus of a set of N agents. In this approach each agent dynamics is represented by a Switched Linear System (SLS). Agent SLS systems are neither constrained to be the same nor to have the same state dimension. In the communication topology, some agents get the reference from the output of a virtual agent, and every agent gets the output information of its neighbors resulting in a connected topology. Using this information, every agent computes the exosystem state to solve its own regulation problem. The approach herein proposed employs a local switched stabilizing feedback for each agent such that it has a common Lyapunov function. Finally, considering this assumption, the existence of a Lyapunov function which ensures the stability of the multi-agent regulation error is demonstrated.

On the decoupling problem of linear multivariable systems by static state feedback

In this paper, the decoupling problem of linear multivariable systems using a static state feedback is considered. Two main contributions related to this problem are presented. The first one is a complete characterization of the decoupled closed-loop structure of a decouplable square linear system. The second contribution is a result presenting necessary and sufficient conditions for a right invertible linear system with no finite zeros to be decouplable with a desirable infinite structure using nonregular state feedback. These conditions are stated in terms of the row image of two real matrices, which are obtained using the extended interactor of the system and the desirable infinity structure of the closed-loop system. Given a system satisfying these conditions, it is shown how to obtain a non regular static state feedback that decouples the system.