Uniform semiglobal practical asymptotic stability for non-autonomous cascaded systems and applications

It is due to the modularity of the analysis that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on ``adding integrators''. Nevertheless, the standing assumptions in most of the present literature on cascaded systems is that, when decoupled, the subsystems constituting the cascade are uniformly globally asymptotically stable (UGAS). Hence existing results fail in the more general case when the subsystems are uniformly semiglobally practically asymptotically stable (USPAS). This situation is often encountered in control practice, e.g., in control of physical systems with external perturbations, measurement noise, unmodelled dynamics, etc. This paper generalizes previous results for cascades by establishing that, under a uniform boundedness condition, the cascade of two USPAS systems remains USPAS. An analogous result can be derived for USAS systems in cascade. Furthermore, we show the utility of our results in the PID control of mechanical systems considering the dynamics of the DC motors.Comment: 16 pages. Modifications 1st Feb. 2006: additional requirement that links the parameter-dependency of the lower and upper bounds on the Lyapunov function, stronger condition of uniform boundedness of solutions, modification and simplification of the proofs accordingl

On the robustness analysis of triangular nonlinear systems: iISS and practical stability

International audienceThis note synthesizes recent results obtained by the authors on the stability and robustness analysis of cascaded systems. It focuses on two properties of interest when dealing with perturbed systems, namely integral input-to-state stability and practical stability. We present sufficient conditions for which each of these notions is preserved under cascade interconnection. The obtained conditions are of a structural nature, which makes their use particularly easy in practice

A system-theoretic framework for privacy preservation in continuous-time multiagent dynamics

In multiagent dynamical systems, privacy protection corresponds to avoid disclosing the initial states of the agents while accomplishing a distributed task. The system-theoretic framework described in this paper for this scope, denoted dynamical privacy, relies on introducing output maps which act as masks, rendering the internal states of an agent indiscernible by the other agents as well as by external agents monitoring all communications. Our output masks are local (i.e., decided independently by each agent), time-varying functions asymptotically converging to the true states. The resulting masked system is also time-varying, and has the original unmasked system as its limit system. When the unmasked system has a globally exponentially stable equilibrium point, it is shown in the paper that the masked system has the same point as a global attractor. It is also shown that existence of equilibrium points in the masked system is not compatible with dynamical privacy. Application of dynamical privacy to popular examples of multiagent dynamics, such as models of social opinions, average consensus and synchronization, is investigated in detail.Comment: 38 pages, 4 figures, extended version of arXiv preprint arXiv:1808.0808

Remote control and motion coordination of mobile robots

As robots destined for personal and professional applications advance towards becoming part of our daily lives, the importance and complexity of the control algorithms which regulate them should not be underestimated. This thesis is related to two fields within robotics which are of major importance in this paradigm shift; namely, telerobotics and cooperative robotics. On the one hand, telerobotic systems support remote or dangerous tasks, whereas, on the other hand, the use of cooperative robotic systems supports distributed tasks and has several advantages with respect to the use of single-robot systems. The use of robotic systems in remote tasks implies in many cases the physical separation of the controller and the robot. This separation is advantageous when carrying out a variety of remote or hazardous tasks, but at the same time constitutes one of the main drawbacks of this type of robotic systems. Namely, as information is being relayed from the controller to the robot and back over the communication network, a time-delay unavoidably appears in the overall control loop. Hence, controller designs which guarantee the stability and performance of the robot even in the presence of the aforementioned time-delay become necessary in order to ensure a safe and reliable completion of the assigned tasks. On the other hand, using a group of robots to carry out a certain assignment, as compared to a single robot, provides several advantages such as an increased flexibility and the ability to complete distributed or more complex tasks. In order to successfully complete their collective task, the robots in the group generally need to coordinate their behavior by mutually exchanging information. When this information exchange takes place over a delay-inducing communication network, the consequences of the resulting time-delay must be taken into account. As a result, it is of great importance to design controllers which allow the group of robots to work together and complete their task in spite of the time-delay affecting their information exchange. The two control problems explained previously are addressed in this thesis. Firstly, the control of wheeled mobile robots over a delay-inducing communication network is considered by studying the remote tracking control problem for a unicycle-type mobile robot with communication delays. The most important issue to consider is that the communication delay in the control loop most probably compromises the performance and stability of the robot. In order to tackle this problem, a state estimator with a predictor-like structure is proposed. The state estimator is based on the notion of anticipating synchronization and, when acting in conjunction with a tracking control law, the resulting control strategy stabilizes the system and mitigates the negative effects of the time-delay. By exploiting existing results on nonlinear cascaded systems with time-delay, the local uniform asymptotic stability of the closed-loop tracking error dynamics is guaranteed up to a maximum admissible time-delay. Ultimately, explicit expressions which illustrate the relationship between the allowable time-delay and the control parameters of the robot are provided. Secondly, the coordination of a group of wheeled mobile robots over a delayinducing communication network is considered by studying the remote motion coordination problem for a group of unicycle-type mobile robots with a delayed information exchange between the robots. Specifically, master-slave and mutual motion coordination are considered. A controller design which allows the robots to maintain motion coordination even in the presence of a time-delay is proposed and the ensuing global stability analysis provides expressions which relate the control parameters of the robot and the allowable time-delay. The thesis places equal emphasis on theoretical developments and experimental results. In order to do so, the proposed control strategies are experimentally validated using the Internet as the communication network and multi-robot platforms located in Eindhoven, The Netherlands and Tokyo, Japan. To summarize, this thesis addresses two related control problems. On the one hand, we consider the tracking control of a wheeled mobile robot over a communication network which induces a time-delay. On the other hand, we focus on the motion coordination of a group of these robots under the consideration that the information exchange between the robots takes place over a delay-inducing communication network

A simple one-to-one communication algorithm for formation-tracking control of mobile robots

International audienceWe solve the formation-tracking control problem for mobile robots via linear control. As in the classical tracking control problem for two nonholonomic systems, the swarm is driven by a fictitious robot which moves about freely. Only one "leader" robot communicates with the reference vehicle and in turn, acts as a leader to a second robot hence forming a fixed spanning tree. We show that a simple condition on the reference angular velocity (persistency of excitation) suffices to achieve consensus tracking