where g : R × R × R → R is a C function. Once we specify a parameter path u(t), t ≥ t1, in the parameter space we can solve (1.1) uniquely for x(t), t ≥ t1, with the given initial condition x(t1) = x0. Alternatively if we specify a parameter path u(t), t ≤ t1, in the parameter space we can solve (1.1) uniquely for x(t), t ≤ t1, with the given terminal condition x(t1) = x0. Suppose now that for ...

A new fundamental solution semigroup for operator differential Riccati equationsis developed. This fundamental solution semigroup is constructed via an auxiliary finite horizonoptimal control problem whose value functional growth with respect to time horizon is determinedby a particular solution of the operator differential Riccati equation of interest. By exploiting semi-convex...

The possibility of achieving a deadbeat regulation and tracking in linear systems independently of their initial conditions is investigated. The attention is focused on single-input single-output control systems incorporating a dynamical sensor in the loop. A necessary and sufficient condition for a deadbeat controller to exist is established. All deadbeat controllers are described in paramet­ ...

This paper presents a novel way of manipulating the initial conditions in the consensus equation such that a constrained agreement problem is solved across a distributed network of agents, particularly for a network represented by a tree graph. The presented method is applied to the problem of coordinating multiple pendula attached to mobile bases. The pendula should move in such a way that the...

While non-smooth approaches (including sliding mode control) provide explicit feedback laws that ensure finite-time stabilization but in terminal time that depends on the initial condition, fixed-time optimal control with a terminal constraint ensures regulation in prescribed time but lacks the explicit character in the presence of nonlinearities and uncertainties. In this paper we present an a...

Robust stabilization of an uncertain system subject to input constraints is addressed without making open-loop stability assumptions. A local approach is taken to nd a robust control law and a set of initial conditions that can be stabilized. A piecewise-linear control law is described. It is generated by a parametrized algebraic Riccati equation of the H 1 control theory. Once system trajector...

Air Traac Management (ATM) of the future allows for the possibility of free ight, in which aircraft choose their own optimal routes, altitudes, and velocities. The safe resolution of trajectory connicts between aircraft is necessary to the success of such a distributed control system. In this paper, we present a method to synthesize provably safe connict resolution maneuvers. The method models ...

An optimal control problem is studied, in which the state is required to remain in a compact set S. A control feedback law is constructed which, for given ε > 0, produces ε-optimal trajectories that satisfy the state constraint universally with respect to all initial conditions in S. The construction relies upon a constraint removal technique which utilizes geometric properties of inner approxi...

This paper analyzes the stability of linear systems with quantized feedback in the presence of a mismatch between the initial conditions at the coder and decoder. Under the assumption of the prefect channel, we show that using the scheme proposed in [Liberzon, Nešić (2007)] it is possible to achieve global exponential stability of linear systems with quantized feedback when the coder and decode...

Adaptive optimal control using value iteration initiated from a stabilizing control policy is theoretically analyzed in terms of stability of the system during the learning stage without ignoring the effects of approximation errors. This analysis includes the system operated using any single/constant resulting control policy and also using an evolving/time-varying control policy. A feature of t...