Time Optimal Control Problem Research Articles

Asymptotics of a Solution to a Singularly Perturbed Time-Optimal Control Problem of Transferring an Object to a Set

Asymptotics of a Solution to a Singularly Perturbed Time-Optimal Control Problem of Transferring an Object to a Set

Deep Learning for Efficient and Optimal Motion Planning for AUVs with Disturbances.

We use the recent advances in Deep Learning to solve an underwater motion planning problem by making use of optimal control tools—namely, we propose using the Deep Galerkin Method (DGM) to approximate the Hamilton–Jacobi–Bellman PDE that can be used to solve continuous time and state optimal control problems. In order to make our approach more realistic, we consider that there are disturbances in the underwater medium that affect the trajectory of the autonomous vehicle. After adapting DGM by making use of a surrogate approach, our results show that our method is able to efficiently solve the proposed problem, providing large improvements over a baseline control in terms of costs, especially in the case in which the disturbances effects are more significant.

Time-optimal control problem for a linear parameter varying system with nonlinear item

In this paper, we considered a time-optimal control problem for a new type of linear parameter varying (LPV) system which is obtained through data identification in the process of dealing with actual problems. The addition of non-linear terms is compensation for the method that does not require linear expansion at the equilibrium point. Since the objective function is the terminal time which is an implicit function concerning decision variables, it is a non-standard optimal control problem with uncertain terminal time. To find the global optimal solution to this problem, firstly, the control parameterization method is used to transform it into a nonlinear optimization problem of parameter selection, and then the modifed particle swarm optimization (PSO) algorithm is combined to solve the equivalent nonlinear programming problem. Numerical examples are used to illustrate the effectiveness of the proposed algorithm.

Synthesis of Optimal Hybrid Systems for Multipurpose Time-Optimal Operation

We consider a time-optimal control problem for a hybrid system of variable dimension. Continuous motion of the system alternates with discrete variations (switchings) at which the dimension of the state space changes. The change of the space of states of the system can occur if the number of control objects changes, which is typical, for example, for the control problems for groups of a variable number of aircrafts. We obtain sufficient conditions for the time-optimal achievement of all purposes by a group of control objects. The application of optimality conditions is demonstrated by academic examples.

Time-Optimal Interception of a Moving Target by a Dubins Car

The problem of intercepting a target moving along a prescribed trajectory by a Dubins caris stated and formalized as a time-optimal control problem with an arbitrary car velocity directionat the interception. The conditions available in the literature under which the optimal trajectoryis a geodesic line drawn from the initial position of the car to the interception point are refined.Algebraic equations for calculating the optimal interception time are obtained. The optimalcontrol is synthesized based on these equations. A software module is developed for constructingthe optimal car trajectories for various target trajectories.

Time optimal control to a partial stochastic differential system with pseudo almost periodic coefficients

In this paper, we study the time optimal control of a class of partial stochastic impulsive functional differential systems with pseudo almost periodic coefficients in the α-norm functional spaces. Firstly, the existence of p-mean piecewise pseudo almost periodic mild solutions for the impulsive stochastic control systems is investigated by utilising stochastic analysis, analytic semigroup, the fixed-point techniques with fractional power arguments. Secondly, the existence of time optimal pairs of a system governed by partial stochastic impulsive functional differential equations is also obtained. Finally, two examples are provided to illustrate the time optimal control problems of parabolic control system with pseudo almost periodic coefficients and impulses.

On time-optimal control problem associated with parabolic equation

On time-optimal control problem associated with parabolic equation

Optimal detumbling trajectory generation and coordinated control after space manipulator capturing tumbling targets

This paper studies a shortest-time dissipation trajectory of a tumbling target after being captured by a space manipulator. A time-optimal control problem (OCP) that considers target attitude motion bounds as well as interaction torque limits at the grasping point is formulated. Then, the state and input inequality constraints are represented as extended dynamical sub-systems and saturation functions, respectively. Thereby, the OCP can be solved using the Calculus of Variations method with a highly accurate solution. Additionally, a coordinated controller using reference accelerations is proposed for the space manipulator, which guarantees that both the target and base spacecraft of the space manipulator can track desired trajectories. Numerical simulations demonstrate the effectiveness of the proposed method.

Синтез оптимального управления группой объектов переменного состава

The article deals with the problem of time-optimal control of a hybrid system of variable dimension. The problem of synthesis of optimal hybrid systems of variable dimension is of theoretical interest, since the problems under consideration differ from the classical problems of optimal control of deterministic systems, and methods for their solution have not been developed. The need for research is determined by modern problems of designing complex aviation and rocket and space systems, and the results obtained have a practical orientation and can be used in the creation of automatic control systems.

A Regularization Approach to Analyze the Time-Optimal Motion of a Mobile Robot under State Constraints using Pontryagin’s Maximum Principle

This work concerns the investigation of time-optimal control problem for a simplified mobile robot model subject to state constraints. In this type of problems, which involve the so-called unicycle dynamics, the well-established regularity conditions with respect to the state constraints are not fulfilled. This fact greatly complicates the analysis of the control problem bearing in mind the use of the maximum principle. Moreover, the difficulty is also due to the presence of a singular control mode with respect to the angular velocity. Herein, a regularization approach is proposed in order to overcome these obstacles. A certain tool for the numerical implementation is developed. The numerical analysis is provided for a sample problem.

Time Optimal Control Studies on COVID-19 Incorporating Adverse Events of the Antiviral Drugs

Abstract COVID -19 pandemic has resulted in more than 257 million infections and 5.15 million deaths worldwide. Several drug interventions targeting multiple stages of the pathogenesis of COVID -19 can significantly reduce induced infection and thus mortality. In this study, we first develop SIV model at within-host level by incorporating the intercellular time delay and analyzing the stability of equilibrium points. The model dynamics admits a disease-free equilibrium and an infected equilibrium with their stability based on the value of the basic reproduction number R 0. We then formulate an optimal control problem with antiviral drugs and second-line drugs as control measures and study their roles in reducing the number of infected cells and viral load. The comparative study conducted in the optimal control problem suggests that if the first-line antiviral drugs show adverse effects, considering these drugs in reduced amounts along with the second-line drugs would be very effective in reducing the number of infected cells and viral load in a COVID-19 infected patient. Later, we formulate a time-optimal control problem with the goal of driving the system from any initial state to the desired infection-free equilibrium state in finite minimal time. Using Pontryagin’s Minimum Principle, it is shown that the optimal control strategy is of the bang-bang type, with the possibility of switching between two extreme values of the optimal controls. Numerically, it is shown that the desired infection-free state is achieved in a shorter time when the higher values of the optimal controls. The results of this study may be very helpful to researchers, epidemiologists, clinicians and physicians working in this field.

Time-Optimal Low-Level Control and Gearshift Strategies for the Formula 1 Hybrid Electric Powertrain

Today, Formula 1 race cars are equipped with complex hybrid electric powertrains that display significant cross-couplings between the internal combustion engine and the electrical energy recovery system. Given that a large number of these phenomena are strongly engine-speed dependent, not only the energy management but also the gearshift strategy significantly influence the achievable lap time for a given fuel and battery budget. Therefore, in this paper we propose a detailed low-level mathematical model of the Formula 1 powertrain suited for numerical optimization, and solve the time-optimal control problem in a computationally efficient way. First, we describe the powertrain dynamics by means of first principle modeling approaches and neural network techniques, with a strong focus on the low-level actuation of the internal combustion engine and its coupling with the energy recovery system. Next, we relax the integer decision variable related to the gearbox by applying outer convexification and solve the resulting optimization problem. Our results show that the energy consumption budgets not only influence the fuel mass flow and electric boosting operation, but also the gearshift strategy and the low-level engine operation, e.g., the intake manifold pressure evolution, the air-to-fuel ratio or the turbine waste-gate position.

Intermittent Feedback Control With Maximum Average Off-Time

An intermittent feedback-based control policy is proposed for rejecting bounded disturbance signals in a continuous, linear time-invariant (LTI) system with distinct and rational eigenvalues. The proposed policy maximizes the average feedback-off time while retaining the state trajectory inside a prespecified safe region. To achieve this, the feedback link is alternatively turned on and off. During feedback-on intervals, the state trajectory is steered to the origin in min–max time and then feedback is turned off for some maximal precomputed duration. The largest subset of the safe region that is invariant under the proposed policy is characterized. The feedback control and the open-loop control in the proposed policy, which are applied during feedback-on and feedback-off intervals, respectively, are obtained by solving certain min–max and max–min time-optimal control problems. It is shown that the proposed policy achieves the abovementioned objective of maximizing the average feedback-off time. An interesting additional feature of this policy is that the optimal control problems in it need to be solved only once offline and, hence, they do not increase the burden of real-time computation.

The Adjoint Method for Time-Optimal Control Problems

Abstract In this article, we discuss a special class of time-optimal control problems for dynamic systems, where the final state of a system lies on a hyper-surface. In time domain, this endpoint constraint may be given by a scalar equation, which we call transversality condition. It is well known that such problems can be transformed to a two-point boundary value problem, which is usually hard to solve, and requires an initial guess close to the optimal solution. Hence, we propose a new gradient-based iterative solution strategy instead, where the gradient of the cost functional, i.e., of the final time, is computed with the adjoint method. Two formulations of the adjoint method are presented in order to solve such control problems. First, we consider a hybrid approach, where the state equations and the adjoint equations are formulated in time domain but the controls and the gradient formula are transformed to a spatial variable with fixed boundaries. Second, we introduce an alternative approach, in which we carry out a complete elimination of the time coordinate and utilize a formulation in the space domain. Both approaches are robust with respect to poor initial controls and yield a shorter final time and, hence, an improved control after every iteration. The presented method is tested with two classical examples from satellite and vehicle dynamics. However, it can also be extended to more complex systems, which are used in industrial applications.

Multistage Time-Optimal Control for Synchronization Process in Electric-Driven Mechanical Transmission With Angle Alignment Considering Torque Response Process

Abstract The synchronization process takes up almost one half of the time of the gear-shifting process, and also influences the impacts between the sleeve and the gear ring. To avoid impacts and reduce time duration, a time-optimal control strategy with angle alignment is necessary for the synchronization process. Moreover, to be better accord with practice, the motor torque response process should be taken into account. The parameters in the torque response process depend on control commands, which makes the control problem a multistage one. To solve these issues, a rule-based control strategy is extracted from the dynamic programming (DP) solution of the multistage time-optimal control problem. To obtain this strategy, the dynamic model for the synchronization process with a modified Sigmoid model to precisely depict the torque response process is first solved. Then, the control problem is formulated as a multistage time-optimal control problem with three states and solved by DP. Based on the DP results, a three-stage and a four-stage rule-based control strategies are extracted for normal operation situation and startup situation, respectively. Finally, through comparative studies, the proposed rule-based control strategy can eliminate the speed difference and angle difference simultaneously with almost the same time of the bang–bang control, while the bang–bang control cannot obtain the zero terminals. Moreover, the proposed control strategy only takes 20 ms more than the pure speed synchronization control in the worst case. It would decrease when the initial speed difference increases.

Minimum time learning model predictive control

SummaryIn this paper we present a Learning Model Predictive Control (LMPC) strategy for linear and nonlinear time optimal control problems. Our work builds on existing LMPC methodologies and it guarantees finite time convergence properties for the closed‐loop system. We show how to construct a time varying safe set and terminal cost function using closed‐loop data. The resulting LMPC policy is time varying and it guarantees recursive constraint satisfaction and non‐decreasing performance. Computational efficiency is obtained by convexifing the time‐varying safe set and time‐varying terminal cost function. We demonstrate that, for a class of nonlinear system and convex constraints, the convex LMPC formulation guarantees recursive constraint satisfaction and nondecreasing performance. Finally, we illustrate the effectiveness of the proposed strategies on minimum time obstacle avoidance and racing examples.

Model-Based Reinforcement Learning for Time-Optimal Velocity Control

Autonomous navigation has recently gained great interest in the field of reinforcement learning. However, little attention was given to the time-optimal velocity control problem, i.e. controlling a vehicle such that it travels at the maximal speed without becoming dynamically unstable (roll-over or sliding). Time optimal velocity control can be solved numerically using existing methods that are based on optimal control and vehicle dynamics. In this letter, we develop a model-based deep reinforcement learning to generate the time-optimal velocity control. Moreover, we introduce a method that uses a numerical solution that predicts whether the vehicle may become unstable and intervenes if needed. We show that our combined model outperforms several baselines as it achieves higher velocities (with only one minute of training) and does not encounter any failures during the training process.

Quantum geometric machine learning for quantum circuits and control

The application of machine learning techniques to solve problems in quantum control together with established geometric methods for solving optimisation problems leads naturally to an exploration of how machine learning approaches can be used to enhance geometric approaches for solving problems in quantum information processing. In this work, we review and extend the application of deep learning to quantum geometric control problems. Specifically, we demonstrate enhancements in time-optimal control in the context of quantum circuit synthesis problems by applying novel deep learning algorithms in order to approximate geodesics (and thus minimal circuits) along Lie group manifolds relevant to low-dimensional multi-qubit systems, such as SU(2), SU(4) and SU(8). We demonstrate the superior performance of greybox models, which combine traditional blackbox algorithms with whitebox models (which encode prior domain knowledge of quantum mechanics), as means of learning underlying quantum circuit distributions of interest. Our results demonstrate how geometric control techniques can be used to both (a) verify the extent to which geometrically synthesised quantum circuits lie along geodesic, and thus time-optimal, routes and (b) synthesise those circuits. Our results are of interest to researchers in quantum control and quantum information theory seeking to combine machine learning and geometric techniques for time-optimal control problems.

Single-Switching Reachable Operation Points in a DC-DC Buck Converter: An Approximation from Time Optimal Control.

In this paper, we study the time optimal control problem in a DC-DC buck converter in the underdamped oscillatory regime. In particular, we derive analytic expressions for the admissible regions in the state space, satisfying the condition that every point within the region is reachable in optimal time with a single switching action. We then make use of the general result to establish the minimum and maximum variation allowed to the load in two predefined design set-ups that fulfills the time optimal single switching criteria. Finally, we make use of numerical simulations to show the performance of the proposed control under changes in the reference voltage and load resistance.

Time Optimal Control of System Governed by a Fractional Stochastic Partial Differential Inclusion with Clarke Subdifferential

This paper investigates the time optimal control problems to a new class of fractional non-instantaneous impulsive stochastic partial differential inclusions with Clarke subdifferential in Hilbert spaces. Firstly, using the fractional calculus, properties of fractional resolvent operators and a fixed-point theorem, the existence of mild solutions for these systems is presented. Secondly, the existence of time optimal control of system governed by fractional stochastic control inclusions with Clarke subdifferential and non-instantaneous impulses is also obtained. Finally, an example is given to illustrate our main results.