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Many safety-critical systems, such as autonomous vehicles and service robots, must achieve high-level task specifications with performance guarantees. Much recent progress toward this goal has been made through an automatic controller synthesis from temporal logic specifications. Existing approaches, however, have been limited to relatively short and simple specifications. Furthermore, existing methods either consider some prior discretization of the state space, deal only with a convex fragment of temporal logic, or are not provably complete. We propose a scalable, provably complete algorithm that synthesizes continuous trajectories to satisfy nonconvex temporal logic over reals (RTL) specifications. We separate discrete task planning and continuous motion planning on-the-fly and harness highly efficient Boolean satisfiability and linear programming solvers to find dynamically feasible trajectories that satisfy nonconvex RTL specifications for high-dimensional systems. The proposed design algorithms are proven sound and complete, and simulation results demonstrate our approach's scalability. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of synchronizing a group of identical linear time-invariant agents that exchange information through a communication network. The agents may only broadcast information at discrete-time instants and the decision to execute a broadcast is based on an event-triggered communication protocol. We prove that with the proposed control architecture the state of each agent converges to and remains in a neighborhood of a desired reference signal and the closed-loop system does not exhibit Zeno solutions. A self-triggered implementation of the proposed event-triggered communication protocol is also derived. [ABSTRACT FROM AUTHOR]

The technical note presents the design of a reference governor that manages directly the state and input references for constrained output regulation problems. In particular, for the class of so-called weakly input redundant linear systems, the proposed method leads to a taxonomy in terms of non-intrusive and intrusive reference governors, on the basis of the effect of reference manipulation on the tracking error. Non-intrusive references constitute a degree of freedom that one can freely select to meet constraint requirements; intrusive references are also assignable during transient, but shall be forced to vanish in steady state in order to achieve exact regulation. A simulation study illustrates the features of the proposed approach in support of the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of constructing a finite bisimulation quotient for a discrete-time switched linear system in a bounded subset of its state space. Given a set of observations over polytopic subsets of the state space and a switched linear system with stable subsystems, the proposed algorithm generates the bisimulation quotient in a finite number of steps with the aid of sublevel sets of a polyhedral Lyapunov function. Starting from a sublevel set that includes the origin in its interior, the proposed algorithm iteratively constructs the bisimulation quotient for the region bounded by any larger sublevel set. We show how this bisimulation quotient can be used for synthesis of switching laws and verification with respect to specifications given as syntactically co-safe Linear Temporal Logic formulae over the observed polytopic subsets. [ABSTRACT FROM AUTHOR]

This technical note deals with a general class of discrete 2-D possibly nonlinear systems based on the Roesser model. We first motivate the introduction of Lyapunov type definitions of asymptotic and exponential stability. This will allow us to introduce and discuss several particularities that cannot be found in 1-D systems. Once this background has been carefully designed, we develop different Lyapunov theorems in order to check asymptotic and exponential stability of nonlinear 2-D systems. Finally we propose the first converse Lyapunov theorem in the case of exponential stability. [ABSTRACT FROM AUTHOR]

This works considers the problem of control of linear systems with input constraints. The notion of control Lyapunov functions (CLFs) is first generalized and relaxed to define a constrained control Lyapunov function (CCLF) and a constructive procedure for CCLF is subsequently presented. [ABSTRACT FROM AUTHOR]

Abstract-In this paper, we study the Poincaré recurrence phenomenon for linear dynamical systems, that is, linear systems whose trajectories return infinitely often to neighborhoods of their initial condition. Specifically, we provide several equivalent notions of Poincaré recurrence and review sufficient conditions for nonlinear dynamical systems that ensure that the system exhibits Poincaré recurrence. Furthermore, we establish necessary and sufficient conditions for Poincaré recurrence in linear dynamical systems. In addition, we show that in the case of linear systems the absence of volume-preservation is equivalent to the absence of Poincaré recurrence implying irreversibility of a dynamical system. Finally, we introduce the notion of output reversibility and show that in the case of linear systems, Poincaré recurrence is a sufficient condition for output reversibility. [ABSTRACT FROM AUTHOR]

Motivated by the fact that determining a feedback solution for the optimal control problem under constraints is a hard task we introduce the concept of relative optimality, roughly optimality for a specific (nominal) plant initial condition. We consider a generic discrete-time finite-horizon constrained optimal control problem for linear systems, and we seek for a state feedback (possibly dynamic) controller. As a fundamental requirement we do not admit preactions or controller-state initialization based on the plant initial state and we assume our controller to be time-invariant. In particular we do not consider controllers simply achieved by the feedforward and tracking of the optimal trajectory. A relatively optimal control is a stabilizing controller such that, if initialized at its zero state, produces the optimal (constrained) trajectory for the nominal initial condition of the plant. We show that one of such controllers is linear, dead-beat, and its order is equal to the length of the horizon minus the plant order, thus, of complexity which is known a priori. Some additional features such as the assignment of the compensator poles to achieve strong stabilization are proposed. We show that, by means of the proposed approach, we can face several problems such as optimal point-to-point operations, optimal impulse response and optimal tracking. [ABSTRACT FROM AUTHOR]