Robustness under saturated feedback: Strong iISS for a class of nonlinear systems

International audienceThis note proposes sufficient conditions under which a nonlinear system can be made Strongly iISS in the presence of actuator saturation. This property, recently proposed as a compromise between the strength of ISS and the generality of iISS, ensures boundedness of all solutions provided that the disturbance magnitude is below a certain threshold. We also show that, under a growth rate condition, the bounded feedback law proposed by Lin and Sontag for the stabilization of the disturbance-free system based on the knowledge of a control Lyapunov function, ensures Strong iISS in the presence of perturbations. We illustrate our findings on the angular velocity control of a spacecraft with limited-power thrusters

Towards ISS disturbance attenuation for randomly switched systems

We are concerned with input-to-state stability (ISS) of randomly switched systems. We provide preliminary results dealing with sufficient conditions for stochastic versions of ISS for randomly switched systems without control inputs, and with the aid of universal formulae we design controllers for ISS-disturbance attenuation when control inputs are present. Two types of switching signals are considered: the first is characterized by a statistically slow-switching condition, and the second by a class of semi-Markov processes.Comment: 6 pages, to appear in the Proceedings of the 46th IEEE Conference on Decision & Control, 200

On a small-gain approach to distributed event-triggered control

In this paper the problem of stabilizing large-scale systems by distributed controllers, where the controllers exchange information via a shared limited communication medium is addressed. Event-triggered sampling schemes are proposed, where each system decides when to transmit new information across the network based on the crossing of some error thresholds. Stability of the interconnected large-scale system is inferred by applying a generalized small-gain theorem. Two variations of the event-triggered controllers which prevent the occurrence of the Zeno phenomenon are also discussed.Comment: 30 pages, 9 figure

On Resilient Control of Nonlinear Systems under Denial-of-Service

We analyze and design a control strategy for nonlinear systems under Denial-of-Service attacks. Based on an ISS-Lyapunov function analysis, we provide a characterization of the maximal percentage of time during which feedback information can be lost without resulting in the instability of the system. Motivated by the presence of a digital channel we consider event-based controllers for which a minimal inter-sampling time is explicitly characterized.Comment: 7 pages, 1 figur

A unified approach to controller design for achieving ISS and related properties

A unified approach to the design of controllers achieving various specified input-to-state stability (ISS) like properties is presented. Both full state and measurement feedback cases are considered. Synthesis procedures based on dynamic programming are given using the recently developed results on controller synthesis to achieve uniform l∞ bound. Our results provide a link between the ISS literature and the nonlinear H∞ design literature. © 2005 IEEE

Universal formula for robust stabilization of affine nonlinear multistable systems

International audienceIn this paper, the problem of robust stabilization of affine nonlinear multistable systems with respect to disturbance inputs is studied. The results are obtained using the framework of input-to-state stability (ISS) and integral input-to-state stability (iISS) for systems with multiple invariant sets. The notions of ISS and iISS control Lyapunov functions as well as the small control property are extended within the multistability framework. It is verified that the universal control formula can be applied to yield the ISS (iISS) property to the closed-loop system. The efficiency of the proposed control Lyapunov function in the multistable sense is illustrated in two academic examples

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

LpL_p-stabilization of integrator chains subject to input saturation using Lyapunov-based homogeneous design

Consider the $n$-th integrator $\dot x=J_nx+\sigma(u)e_n$, where $x\in\mathbb{R}^n$, $u\in \mathbb{R}$, $J_n$ is the $n$-th Jordan block and $e_n=(0\ \cdots 0\ 1)^T\in\mathbb{R}^n$. We provide easily implementable state feedback laws $u=k(x)$ which not only render the closed-loop system globally asymptotically stable but also are finite-gain $L_p$-stabilizing with arbitrarily small gain. These $L_p$-stabilizing state feedbacks are built from homogeneous feedbacks appearing in finite-time stabilization of linear systems. We also provide additional $L_\infty$-stabilization results for the case of both internal and external disturbances of the $n$-th integrator, namely for the perturbed system $\dot x=J_nx+e_n\sigma (k(x)+d)+D$ where $d\in\mathbb{R}$ and $D\in\mathbb{R}^n$

Autonomous Behaviors With A Legged Robot

Over the last ten years, technological advancements in sensory, motor, and computational capabilities have made it a real possibility for a legged robotic platform to traverse a diverse set of terrains and execute a variety of tasks on its own, with little to no outside intervention. However, there are still several technical challenges to be addressed in order to reach complete autonomy, where such a platform operates as an independent entity that communicates and cooperates with other intelligent systems, including humans. A central limitation for reaching this ultimate goal is modeling the world in which the robot is operating, the tasks it needs to execute, the sensors it is equipped with, and its level of mobility, all in a unified setting. This thesis presents a simple approach resulting in control strategies that are backed by a suite of formal correctness guarantees. We showcase the virtues of this approach via implementation of two behaviors on a legged mobile platform, autonomous natural terrain ascent and indoor multi-flight stairwell ascent, where we report on an extensive set of experiments demonstrating their empirical success. Lastly, we explore how to deal with violations to these models, specifically the robot\u27s environment, where we present two possible extensions with potential performance improvements under such conditions