Related papers: Time Optimal Synthesis for Left--Invariant Control…
For $\alpha\in(0,\pi/2)$, let $(\Sigma)_\alpha$ be the control system $\dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $u\in [-1,1]$ and $F,G$ are $3\times3$ skew-symmetric matrices generating rotations with…
For the time optimal control on an invariant system on SU(2), with two independent controls and a bound on the norm of the control, the extremals of the maximum principle are explicit functions of time and the resulting differential…
We consider a quantum control problem involving a spin-1/2 particle in a magnetic field. The magnitude of the field is held constant, and the direction of the field, which is constrained to lie in the x-y plane, serves as a control…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
We present an algebraic framework to study the time-optimal synthesis of arbitrary unitaries in SU(2), when the control set is restricted to rotations around two non-parallel axes in the Bloch sphere. Our method bypasses commonly used…
In this contribution, we introduce an efficient method for solving the optimal control problem for an unconstrained nonlinear switched system with an arbitrary cost function. We assume that the sequence of the switching modes are given but…
In this paper we consider the minimum time population transfer problem for a two level quantum system driven by {\em two} external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave…
We present a method for synthesizing controllers to steer trajectories from an initial set to a target set on a finite time horizon. The proposed control synthesis problem is decomposed into two steps. The first step under-approximates the…
This paper addresses the problem of control synthesis for nonlinear optimal control problems in the presence of state and input constraints. The presented approach relies upon transforming the given problem into an infinite-dimensional…
In this paper, we study time-optimal control problems related to system of two coupled qubits where the time scales involved in performing unitary transformations on each qubit are significantly different. In particular, we address the case…
In this paper, we study the design of pulse sequences for NMR spectroscopy as a problem of time optimal control of the unitary propagator. Radio frequency pulses are used in coherent spectroscopy to implement a unitary transfer of state.…
We consider the problem of designing a feedback controller for a multivariable linear time-invariant system which regulates an arbitrary system output to the solution of an equality-constrained convex optimization problem despite unknown…
Autonomous control systems use various sensors to decrease the amount of uncertainty under which they operate. While providing partial observation of the current state of the system, sensors require resources such as energy, time and…
This paper considers the optimal control for hybrid systems whose trajectories transition between distinct subsystems when state-dependent constraints are satisfied. Though this class of systems is useful while modeling a variety of…
Sums-of-squares (SOS) optimization is a promising tool to synthesize certifiable controllers for nonlinear dynamical systems. Building upon prior works, we demonstrate that SOS can synthesize dynamic controllers with bounded suboptimal…
In this paper we solve two equivalent time optimal control problems. On one hand, we design the control field to implement in minimum time the SWAP (or equivalent) operator on a two-level system, assuming that it interacts with an…
We consider the time optimal stabilization problem for a nonlinear control system $\dot x=f(x,u)$. Let $\tau(y)$ be the minimum time needed to steer the system from the state $y\in\R^n$ to the origin, and call $\A(T)$ the set of initial…
We study the problem of estimating the value function of discrete-time switched systems under arbitrary switching. Unlike the switched LQR problem, where both inputs and mode sequences are optimized, we consider the case where switching is…
Time-optimal control for high-order chain-of-integrator systems with full state constraints remains an open and challenging problem within the discipline of optimal control. The behavior of optimal control in high-order problems lacks…
We introduce a metric that can quantify the temporal relaxation of Signal Temporal Logic (STL) specifications and facilitate resilient control synthesis in the face of infeasibilities. The proposed metric quantifies a cumulative notion of…