Related papers: Direct Pseudospectral Optimal Control by Orthogona…
We propose a neural network approach to model general interaction dynamics and an adjoint based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem…
Pseudospectral collocation methods have proven to be powerful tools to solve optimal control problems. While these methods generally assume the dynamics is given in the first order form $\dot{x} = f (x, u, t)$, where x is the state and u is…
Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…
In [1], we inaugurated a new area of optimal control (OC) theory that we called "periodic fractional OC theory," which was developed to find optimal ways to periodically control a fractional dynamic system. The typical mathematical…
In this work we propose a coverage planning control approach which allows a mobile agent, equipped with a controllable sensor (i.e., a camera) with limited sensing domain (i.e., finite sensing range and angle of view), to cover the surface…
As we move to increasingly complex cyber-physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal…
In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very…
Classical approximation bases such as Chebyshev polynomials provide principled and interpretable representations, but their multivariate tensor-product constructions scale exponentially with dimension and impose axis-aligned structure that…
The well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Differential Equations (ODEs). Such problems naturally arise as…
This paper investigates optimal control problems formulated over a class of piecewise-smooth vector fields. Instead of optimizing over the discontinuous system directly, we instead formulate optimal control problems over a family of…
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…
Existing algorithms for the optimal control of quantum observables are based on locally optimal steps in the space of control fields, or as in the case of genetic algorithms, operate on the basis of heuristics that do not explicitly take…
This paper presents a trajectory optimization and control approach for the guidance of an orbital four-arm robot in extravehicular activities. The robot operates near the target spacecraft, enabling its arm's end-effectors to reach the…
In this paper, a novel design scheme is introduced to solve the optimal control problem for nonlinear systems with unsymmetrical and state-dependent input constraints. By introducing an initial stabilizing control policy as the baseline of…
We consider the optimal control problem governed by diffusion convection reaction equation without control constraints. The proper orthogonal decomposition(POD) method is used to reduce the dimension of the problem. The POD method may be…
This work investigates the optimal control of the variable-exponent subdiffusion, which extends the work [Gunzburger and Wang, {\it SIAM J. Control Optim.} 2019] to the variable-exponent case to account for the multiscale and crossover…
This work develops feasible path trajectories for a coordinated strike with multiple aircraft in a constrained environment. Using direct orthogonal collocation methods, the two-point boundary value optimal control problem is transcribed…
This paper presents a novel approach for collision avoidance in optimal and model predictive control, in which the environment is represented by a large number of points and the robot as a union of padded polygons. The conditions that none…
We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of Optimal Control Problems (OCPs) constrained by random partial…
Piecewise Polynomials (PPs) are utilized in several engineering disciplines, like trajectory planning, to approximate position profiles given in the form of a set of points. While the approximation target along with domain-specific…