A new method is developed for accurately approximating the solution to state-variable inequality path constrained optimal control problems using a multiple-domain adaptive Legendre-Gauss-Radau collocation method. The method consists of the following parts. First, a structure detection method is developed to estimate switch times in the activation and deactivation of state-variable inequality path constraints. Second, using the detected structure, the domain is partitioned into multiple-domains where each domain corresponds to either a constrained or an unconstrained segment. Furthermore, additional decision variables are introduced in the multiple-domain formulation, where these additional decision variables represent the switch times of the detected active state-variable inequality path constraints. Within a constrained domain, the path constraint is differentiated with respect to the independent variable until the control appears explicitly, and this derivative is set to zero along the constrained arc while all preceding derivatives are set to zero at the start of the constrained arc. The time derivatives of the active state-variable inequality path constraints are computed using automatic differentiation and the properties of the chain rule. The method is demonstrated on two problems, the first being a benchmark optimal control problem which has a known analytical solution and the second being a challenging problem from the field of aerospace engineering in which there is no known analytical solution. When compared against previously developed adaptive Legendre-Gauss-Radau methods, the results show that the method developed in this paper is capable of computing accurate solutions to problems whose solution contain active state-variable inequality path constraints.
For this study, we focus on the exploration of maritime areas that contain accident-prone points, such as illegal riding, unauthorized boarding, illegal fishing, and smuggling. This exploration is carried out using a cooperative system consisting of an Unmanned Aerial Vehicle (UAV) and an Unmanned Surface Vehicle (USV). The goal is to allow the USV-UAV system to efficiently explore all of the accident-prone points while minimizing the UAV’s energy usage. Specifically, we aim to achieve this objective while keeping travel time as short as possible. The collaborative exploration system leverages the strengths of both the UAV and the USV. The UAV is deployed to explore hazardous areas that are inaccessible by the USV, while the USV doubles as a mobile charging station, resolving the UAV’s energy limitation issue. The proposed algorithm for this subject paper, called the Collaborative Accident Searching Routing Optimization (CASRO) algorithm, utilizes the benefits of both the Lazy Theta* algorithm and the Improved Ant Colony algorithm to optimize the path of a cooperative system between USV and UAV. With CASRO, we aim to address the two key limitations of the USV, namely poor flexibility, and the UAV’s limited energy simultaneously. Finally, the effectiveness and superiority of the proposed planning strategy in target exploration is verified by numerical simulations of randomly distributed maritime areas with accident-prone points.
This paper proposes a new cost criterion to enhance the precision of a zonotopic state estimator for discrete-time descriptor linear systems. Originally, the algorithm solves a minimum-trace problem involving zonotopes, whose evolution is given by an interval observer structure containing extra design matrices, called degrees of freedom. Although the minimization of trace yields explicit solutions, it does not necessarily imply minimization of volume, and thereby, the precision of the output zonotope cannot be improved effectively. The volume measure for zonotopes is computationally expensive and, when used as cost criterion, implies nonlinear optimization problems. Motivated by such issues, we here propose a minimum-radius criterion where the smallest box enclosing the output zonotope is minimized. The resulting optimization problem is nonlinear, but its convexity is exploited to yield an equivalent linear program. The effectiveness of our approach is illustrated over two numerical examples.
In this paper, we study the optimal control of a discrete-time stochastic differential equation (SDE) of mean-field type, where the coefficients can depend on both a function of the law and the state of the process. We establish a new version of the maximum principle for discrete-time mean-field type stochastic optimal control problems. Moreover, the cost functional is also of the mean-field type. This maximum principle differs from the classical principle one since we introduce new discrete-time mean-field backward (matrix) stochastic equations. Based on the discrete-time mean-field backward stochastic equations where the adjoint equations turn out to be discrete backward SDEs with mean field, we obtain necessary first-order and sufficient optimality conditions for the stochastic discrete mean-field optimal control problem. To verify, we apply the result to production and consumption choice optimization problem.
It is well known that conservative mechanical systems exhibit local oscillatory behaviours due to their elastic and gravitational potentials, which completely characterise these periodic motions together with the inertial properties of the system. The classification of these periodic behaviours and their geometric characterisation are in an on-going secular debate, which recently led to the so-called eigenmanifold theory. The eigenmanifold characterises nonlinear oscillations as a generalisation of linear eigenspaces. With the motivation of performing periodic tasks efficiently, we use tools coming from this theory to construct an optimization problem aimed at inducing desired closed-loop oscillations through a state feedback law. We solve the constructed optimization problem via gradient-descent methods involving neural networks. Extensive simulations show the validity of the approach.
We introduce the theoretical framework from geometric optimal control for a control system modeled by the Generalized Lotka-Volterra (GLV) equation, motivated by restoring the gut microbiota infected by Clostridium difficile combining antibiotic treatment and fecal injection. We consider both permanent control and sampled-data control related to the medical protocols.