On the Optimal Balanced-Energy Formation Flying Maneuvers

In this paper, the nonlinear optimal control problem is investigated for spacecraft formation flying with collision avoidance. Based on a nonlinear model of formation flying, two optimal tracking control laws are proposed to ensure the formation pattern converges to the predetermined configuration. The first optimal control law which combines Lyapunov optimizing control with a trajectory-following optimization technique is developed to solve the finite-time nonlinear optimal control problem. For the second controller, an extended [Formula: see text]-[Formula: see text] method is applied to design a closed-form feedback control scheme for nonlinear control problem of spacecraft formation flying with non-standard cost functions. By taking into account the flying safety, a repulsive control scheme is incorporated in the optimal controller to ensure collision avoidance and minimize the performance index. Finally, a numerical example is performed to demonstrate the effectiveness of the proposed approaches.

Formation Flying is revolutionizing Earth and Space science and the way the space community conducts science missions. This technological transformation provides new, innovative techniques in spacecraft guidance, navigation, and control, and how the science community gathers and shares information between space vehicles and the ground. These technologies will also expedite the human exploration of space. Once fully matured, this technology will result in swarms of space vehicles flying as virtual platforms or distributed space systems and sensor webs which gather significantly more and better science data than is possible today. Formation flying will be enabled through the development and deployment of automated spaceborne guidance, navigation, and control (GN&C) systems integrated with intrasatellite communications infrastructure. Innovative spacecraft autonomy techniques, such as differential Global Positioning System (GPS) technology, optical, and vision-based navigation and celestial navigation allow autonomous navigation while other technologies provide for the autonomous control methods to maintain and optimize these formations. This paper provides a vision of the future of space exploration in the context of GN&C technology, and an overview of the current status of NASA technology development and its partnerships with the Department of Defense (DoD), Industry, and University to bring formation flying technology to the forefront as quickly as possible. We address the impediments that need to be overcome to achieve the distributive spacecraft vision and NASA GSFC's approach to transfer this technology to space. We will also describe some of the formation flying testbeds, such as the on-orbit Air Force Research Laboratory (AFRL) University Nanosats, and Orion test beds and ground based GSFC Formation Flying Test Bed, which are being developed to demonstrate and validate innovative position sensing and formation control technologies.

Adaptive optimal backstepping control for strict-feedback nonlinear systems with time-varying partial output constraints

Robust [formula omitted] optimal safety control for WMR system with disturbances and actuator attack under event conditions

In this paper, we study the optimal control problem for Takagi–Sugeno (T-S) fuzzy systems with disturbances. Due to the presence of disturbances in the T-S fuzzy systems, a fuzzy optimal state feedback control approach is presented by employing a two-player zero-sum game. Since the analytical optimal control solutions and the worst-case disturbance policies of T-S fuzzy systems can be boiled down to solving the algebraic Riccati equations (AREs), which are difficult to be obtained directly, a model-free policy iteration (PI) learning algorithm is proposed to obtain their approximation solutions. It is proved that the developed fuzzy optimal state feedback controller can ensure the fuzzy systems to be asymptotically stable and satisfy the disturbance attenuation condition simultaneously. Also, the designed PI learning algorithm can converge to their optimal solutions. Finally, we apply the developed fuzzy optimal state feedback control method to the truck-trailer system and the simulation results demonstrated the effectiveness of the developed scheme.

Data mining approach for improving the optimal control of HVAC systems: An event-driven strategy

1 A Survey on Computational Optimal Control.- Issues in the Direct Transcription of Optimal Control Problems to Sparse Nonlinear Programs.- Optimization in Control of Robots.- Large-scale SQP Methods and their Application in Trajectory Optimization.- Solving Optimal Control and Pursuit-Evasion Game Problems of High Complexity.- 2 Theoretical Aspects of Optimal Control and Nonlinear Programming.- Continuation Methods In Boundary Value Problems.- Second Order Optimality Conditions for Singular Extremals.- Synthesis of Adaptive Optimal Controls for Linear Dynamic Systems.- Control Applications of Reduced SQP Methods.- Time Optimal Control of Mechanical Systems.- 3 Algorithms for Optimal Control Calculations.- Second Order Algorithm for Time Optimal Control of a Linear System.- An SQP-type Solution Method for Constrained Discrete-Time Optimal Control Problems.- Numerical Methods for Solving Differential Games, Prospective Applications to Technical Problems.- Construction of the Optimal Feedback Controller for Constrained Optimal Control Problems with Unknown Disturbances.- Repetitive Optimization for Predictive Control of Dynamic Systems under Uncertainty.- Optimal Control of Multistage Systems Described by High-Index Differential-Algebraic Equations.- A New Class of a High Order Interior Point Method for the Solution of Convex Semiinfinite Optimization Problems.- A Structured Interior Point SQP Method for Nonlinear Optimal Control Problems.- 4 Software for Optimal Control Calculations.- Automated Approach for Optimizing Dynamic Systems.- ANDECS: A Computation Environment for Control Applications of Optimization.- Application of Automatic Differentiation to Optimal Control Problems.- OCCAL: A mixed symbolic-numeric Optimal Control CALculator.- 5 Applications of Optimal Control.- A Robotic Satellite with Simplified Design.- Nonlinear Control under Constraints of a Biological System.- An Object-Oriented Approach to Optimally Describe and Specify a SCADA System Applied to a Power Network.- Near-Optimal Flight Trajectories Generated by Neural Networks.- Performance of a Feedback Method with Respect to Changes in the Air-Density during the Ascent of a Two-Stage-To-Orbit Vehicle.- Linear Optimal Control for Reentry Flight.- Steady-State Modelling of Turbine Engine with Controllers.- Shortest Paths for Satellite Mounted Robot Manipulators.- Optimal Control of the Industrial Robot Manutec r3.

Optimal control of fractional order systems is a long established domain of fractional calculus. Nevertheless, it relies on equations expressed in terms of pseudo-state variables which raise fundamental questions. So in order remedy these problems, the authors propose in this paper a new and original approach to fractional optimal control based on a frequency distributed representation of fractional differential equations called the infinite state approach, associated with an original formulation of fractional energy, which is intended to really control the internal system state. In the first step, the fractional calculus of variations is revisited to express appropriate Euler Lagrange equations. Then, the quadratic optimal control of fractional linear systems is formulated. Thanks to a frequency discretization technique, the previous theoretical equations are converted into an equivalent large dimension integer order system which permits the implementation of a feasible optimal solution. A numerical example illustrates the validity of this new approach.

This paper studies the decentralized optimal control of discrete-time system with inputdelay, where a large number of agents with the identical decoupling dynamical equations and the coupling cost function through the mean field are considered. The decentralized and centralized optimal controllers are proposed by the optimal tracking control of LQR problem with delay. They are proved that the optimal controllers and the optimal cost function of the centralized and decentralized solutions are equivalent for the optimal control problem. An illustrative example is given to show the efficiency of the decentralized optimal controllers.

In this study, a finite‐time online optimal controller was designed for a nonlinear wheeled mobile robotic system (WMRS) with inequality constraints, based on reinforcement learning (RL) neural networks. In addition, an extended cost function, obtained by introducing a penalty function to the original long‐time cost function, was proposed to deal with the optimal control problem of the system with inequality constraints. A novel Hamilton‐Jacobi‐Bellman (HJB) equation containing the constraint conditions was defined to determine the optimal control input. Furthermore, two neural networks (NNs), a critic and an actor NN, were established to approximate the extended cost function and the optimal control input, respectively. The adaptation laws of the critic and actor NN were obtained with the gradient descent method. The semi‐global practical finite‐time stability (SGPFS) was proved using Lyapunov's stability theory. The tracking error converges to a small region near zero within the constraints in a finite period. Finally, the effectiveness of the proposed optimal controller was verified by a simulation based on a practical wheeled mobile robot model.

In this paper, an iterative adaptive dynamic programming (ADP) algorithm is developed to solve the optimal cooperative control problems for residential multi-battery systems. To avoid solving high-dimensional optimal control problems, we first constrain all the batteries at their worst performance, which transforms the multi-input optimal control problem into a single-input one. Based on the worst-performance optimal control law, the optimal cooperative control law for the residential multi-battery systems is obtained, where in each iteration, only a single-input optimization problem is implemented. Finally, numerical results are given to illustrate the performance of the developed algorithm.

Optimal control strategies are very useful in manipulation problems of robots. However, most optimal controls are highly sensitive to plant-parameter variations and disturbances because optimal controls try to pick up exact information from the mathematical models in order to realize the best performance. We recognize that difficulties are involved in exact modeling of plants and prevention of disturbances. Therefore, we need a optimal control method with low sensitivity. The ideas of closed-loop control system design using LQG/TR techniques (linear quadratic Gaussian control with transfer recovery) are discussed in this paper. We combine optimal controls and LQG/TR control into two-degrees-of-freedom control systems to reduce the sensitivities of optimal control strategies. In digital simulations, we obtained excellent results of a two-link manipulator in an optimal time control problem using our method. Some modeling errors and considerable disturbances are allowed in the method. Thus, we can realize good performances in practical manipulation problems using our method.

The numerical solution of the optimal control and trajectory of systems with hard control bounds is considered. A new algorithm, which extends the gradient method [1] to systems with hard control bounds is presented. The algorithm is based on the use of an adjustable control-variation weight (ACW) matrix to enforce the bounds. The application of the algorithm to the minimum-time control of a two-link robot arm is presented as an example.

This paper considers the global optimal control for nonlinear interconnected large-scale systems with respect to linear quadratic functional. A successive approximation procedure is proposed to design the feedforward feedback nearly optimal control law. By introducing the Successive Approximation Approach of the nonlinear differential equation theory, a nonhomogeneous linear two-point boundary value problem sequence is constructed to approximate the nonlinear large-scale two-point boundary value problem, which is the necessary condition of the nonlinear control problem. By iteratively solving this nonhomogeneous linear approximating sequence, a global nearly optimal control law that composed of a linear closed-loop feedback compensatory term and an open-loop feedforward compensatory term is designed. An algorithm is presented to design certain qualified nearly optimal control law by truncating an infinite iteration result. An illustrative example shows the validity of the algorithm.

Stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses