This work presents a general theory for the construction of a polyhedral outer approximation of the reachable set (“polyhedral bounds”) of a dynamic system subject to time-varying inputs and uncertain initial conditions. This theory is inspired by the efficient methods for the construction of interval bounds based on comparison theorems. A numerically implementable instance of this theory leads...

We study the local exponential stabilization of the 3D NavierStokes equations in a bounded domain, around a given steady-state flow, by means of a boundary control. We look for a control so that the solution to the Navier-Stokes equation be a strong solution. In the 3D case, such solutions may exist if the Dirichlet control satisfies a compatibility condition with the initial condition. In orde...

We present a logic-based approach for analysing event-based requirements specifications given in terms of a system’s reaction to events and safety properties. The approach uses an event-based logic, called the Event Calculus, to represent such specifications declaratively. Building on this formalism, the approach uses an abductive reasoning mechanism for analysing safety properties. Given a sys...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii CHAPTER 1. INTRODUCTIOIN . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Robust Feedback Linearization . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Application to Hydraulic System . . . . . . . . . . . . . . . . . . . . . . 5...

A LDP is proved for the inviscid shell model of turbulence. As the viscosity coefficient ν converges to 0 and the noise intensity is multiplied by √ ν, we prove that some shell models of turbulence with a multiplicative stochastic perturbation driven by a H-valued Brownian motion satisfy a LDP in C([0, T ], V) for the topology of uniform convergence on [0, T ], but where V is endowed with a top...

This paper presents a relaxed scheme for controller synthesis of continuous-time systems in the Takagi-Sugeno form, based on non-quadratic Lyapunov functions and a non-PDC control law. The relaxations here provided allow state and input dependence of the membership functions’ derivatives, as well as independence on initial conditions when input constraints are needed. Moreover, the controller s...

This paper studies regional boundary stabilization of nonlinear Schrödinger equation with state delay and bounded internal disturbance. The boundary constrained control law is designed by using the backstepping method. Regional input-tostate stability (ISS) of the perturbed system with time-delay is established by a Lyapunov function and a generalized Halanay’s inequality. Estimates on the set ...

Given an x0 ∈ Rn we study the infinite horizon problem of minimizing the expression ∫ T 0 f(t, x(t), x ′(t))dt as T grows to infinity where x : [0,∞) → Rn satisfies the initial condition x(0) = x0. We analyse the existence and the properties of approximate solutions for every prescribed initial value x0. We also establish that for every bounded set E ⊂ Rn the C([0, T ]) norms of approximate sol...

It was shown in Spong [1999b] that the passive gaits for a planar 2DOF biped walking on a shallow slope (Goswami et al. [1995]) can be made slope invariant by a passivity based control that compensates only the gravitational torques acting on the biped. In this paper we extend these results to the general case of a 3-D, n-DOF robot. We show that if there exists a passive walking gait, i.e., if ...

Multiple-pursuer multiple-evader games raise fundamental and novel problems in control theory and robotics. In this paper, we propose a distributed solution to this problem that simultaneously addresses the discrete assignment of pursuers to evaders as well as the continuous control strategies for capturing individual evaders. The resulting hybrid controller for each pursuer consists of both lo...