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Given a finite-dimensional time continuous control system and $\varepsilon>0$, we address the question of the existence of controls that maintain the corresponding state trajectories in the $\varepsilon$-neighborhood of any prescribed path…
We consider an exit-time minimum problem with a running cost, $l\geq 0$ and unbounded controls. The occurrence of points where $l=0$ can be regarded as a transversality loss. Furthermore, since controls range over unbounded sets, the family…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
We provide simple necessary and sufficient conditions under which a path constitutes a solution to an infinite-horizon, continuous-time optimal control problem. We prove transversality conditions under standard assumptions. We also present…
In this paper we address the problem of tracking control of nonlinear systems via contraction analysis. The necessary conditions of the systems which can achieve universal asymptotic tracking are studied under several different cases. We…
This paper develops a new approach to small time local attainability of smooth manifolds of any dimension, possibly with boundary and to prove H\"older continuity of the minimum time function. We give explicit pointwise conditions of any…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…
The sequential compactness afforded hybrid systems under mild regularity constraints guarantee outer/upper semicontinuous dependence of solutions on initial conditions and perturbations. For reachable sets of hybrid systems, this property…
In this article, we give a condition for the global controllability of affine nonlinear control systems with drifts on Euclidean spaces. Under regularity assumptions, the condition is necessary and sufficient in the codimension-1 and…
When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely, singular minimizing trajectories of the…
We investigate optimal control of dynamical systems which are affine, i.e., linear in control, but nonlinear in state. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible, a task…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
The existence of a Control Barrier Function (CBF) for a control-affine system provides a powerful design tool to ensure safety. Any controller that satisfies the CBF condition and ensures that the trajectories of the closed-loop system are…
We present exact analytical solutions to the classical equations of motion and analyze the dynamical consequences of the existence of a minimal length for the free particle, particle in a linear potential, anti-symmetric constant force…
Structural symmetries of linear dynamical systems can be exploited for decoupling the dynamics and reducing the computational complexity of the controller implementation. However, in practical applications, inexact structural symmetries…
In this paper, we propose a new control design scheme for solving the obstacle avoidance problem for nonlinear driftless control-affine systems. The class of systems under consideration satisfies controllability conditions with iterated Lie…
The paper is concerned with mechanical systems which are controlled by implementing a number of time-dependent, frictionless holonomic constraints. The main novelty is due to the presence of additional non-holonomic constraints. We develop…
The paper deals with systems of ordinary differential equations containing in the right-hand side controls which are discontinuous in phase variables. These controls cause the occurrence of sliding modes. If one uses one of the well-known…
This paper considers the problem of minimal control inputs to affect the system states such that the resulting system is structurally controllable. This problem and the dual problem of minimal observability are claimed to have no…
This paper studies the design of controllers for discontinuous dynamics that ensure the safety of non-smooth sets. The safe set is represented by arbitrarily nested unions and intersections of 0-superlevel sets of differentiable functions.…