Data-physics fused robust inertia matching for optimal attitude control in TBM under time scale

In this paper, a neural network based optimal adaptive attitude control scheme is derived for the near-space vehicle with uncertainties and external time-varying disturbances. Firstly, radial basis function neural network (RBFNN) approximation method and nonlinear disturbance observer (NDO) are used to tackle the system uncertainties and external disturbances, respectively. Subsequently, a feedforward control input under backstepping control frame with RBFNN and NDO is designed to transform the optimal tracking control problem into an optimal stabilization problem. Then, a single online approximation based adaptive method is used to learn the Hamilton–Jacobi–Bellman equation to obtain the corresponding optimal controller. As a result, the compound controller consists of feedforward control input and optimal controller which can ensure that the near-space vehicle attitude angles are able to track reference signals in an optimal way. Lyapunov stability analysis method is used to show that all the closed-loop system signals are uniformly ultimately bounded. Finally, simulation results show the effectiveness of the proposed optimal attitude control scheme.

Optimal nonlinear control remains one of the most challenging subjects in control theory despite a long research history. In this paper, we present a geometric optimal control approach, which circumvents the tedious task of numerically solving online the Hamilton Jacobi Bellman (HJB) partial differential equation, which represents the dynamic programming formulation of the nonlinear global optimal control problem. Our approach makes implementation of nonlinear optimal attitude control practically feasible with low computational demand onboard a satellite. Optimal stabilizing state feedbacks are obtained from the construction of a control Lyapunov function. Based on a phase space analysis, two natural dual optimal control objectives are considered to illustrate the application of this approach to satellite attitude control: Minimizing the norm of the control torque subject to a constraint on the convergence rate of a Lyapunov function, then maximizing the convergence rate of a Lyapunov function subject to a constraint on the control torque. Both approaches provide ease of implementation and achieve robust optimal trade-offs between attitude control rapidity and torque expenditure, without computational issues.

In this article we aim to maximize the net energy a solar-powered spacecraft gains when performing a maneuver. The net energy can be defined as the integral of the power supplied by the solar panels minus the power used by the attitude control system, and is important since energy is a scarce resource in space. Previous research on optimal attitude control has focused on optimization with respect to other costs, such as time-optimal control and optimal attitude control with respect to the integral of the square of the input. The energy flow depends on both the power spent on actuation and the power received from the solar panels. Thus, the optimal attitude control problem should be formulated in such a way that the attitude of the spacecraft relative to the Sun during the maneuver is included in the calculations. This paper proposes a cost function based on net power to address this problem, introducing a new cost function that incorporates the incoming energy from the solar irradiance and the outgoing energy due to actuation. A simulation study comparing an optimal control solution of the proposed net power cost function using IPOPT in CasADi is presented for a 6U CubeSat equipped with solar cell arrays, where the net power based optimal control maneuver is shown to compare favorably to a sun-pointing PD controller.

Nonlinear optimal feedback control of the complete, three-axis, asymmetric spacecraft attitude dynamics and kinematics is presented. The kinematics description is via minimal modified Rodrigues parameters, which allow nonsingular formulation for eigenaxis rotations greater than 180 degrees. The optimality condition is obtained through Hamilton-Jacobi formulation for the minimization of a cost function in terms of rotational velocities, kinematic parameters, and control torques. A positive-definite Lyapunov function is derived analytically for asymptotic stability. Numerical simulation results for rigid spacecraft undergoing large rotational maneuvers with the present nonlinear controller are compared to a semi-optimal controller and a terminal-time weighted nonlinear optimal controller. With appropriate design parameters, the present nonlinear optimal controller is seen to be globally stabilizing for arbitrarily large initial conditions, whereas the semi-optimal controllers are rendered non-stabilizing. Although being based on an infinite-interval formulation, the present controller is seen to produce a comparable performance with that of the terminal-time weighted optimal controller. In terms of onboard computational resource requirements, the present controller lies between the semi-optimal and the terminal-time weighted optimal controllers.

Energy optimal spacecraft attitude control subject to convergence rate constraints

Robust optimal sliding mode control for spacecraft position and attitude maneuvers

Matrix quadratic equation solution derivation applied in finding steady state solutions of Riccati differential equations with constant coefficients

Features Discusses economic optimization of greenhouse control through mathematical modeling Examines 30 years of scientific research to present a unified framework for efficient decision-making Presents modern methods of control and optimization including classical rule-based and multivariable feedback controllers Utilizes real and experimental examples and novel case discussions such as solar greenhouses Concludes with a discussion of open issues to stimulate new areas of research and development Summary Greenhouse control system manufacturers produce equipment and software with hundreds of settings and, while they hold training courses on how to adjust these settings, there is as yet no integrated instruction on when or why. Despite rapid growth in the greenhouse industry, growers are still faced with a multitude of variables and no unifying framework from which to choose the best option. Consolidating 30 years of research in greenhouse climate control, Optimal Control of Greenhouse Cultivation utilizes mathmatical models to incorporate the wealth of scientific knowledge into a feasible optimal control methodology for greenhouse crop cultivation. Discussing several different paradigms on greenhouse climate control, it integrates the current research into physical modeling of the greenhouse climate in response to heating, ventilation, and other control variables with the biological modeling of variables such as plant evapo-transpiration and growth. Key topics include state-space greenhouse and crop modeling needed for the design of integrated optimal controllers that exploit rather than mitigate outside weather conditions, especially sunlight, given widely different time scales. The book reviews classical rule-based and multivariable feedback controllers in comparison with the optimal hierarchical control paradigm. It considers real and hypothetical examples including lettuce, tomato, and solar greenhouses and examines experimental results of greenhouse climate control using optimal control software. The book concludes with a discussion of open issues as well as future perspectives and challenges. Providing a tool to automatically determine the most economical controls and settings for their operation, this much-needed book relieves growers of unnecessary control tasks, and allows them to achieve the best possible trade-off between short term savings and optimal harvest yield.

In this paper, a robust and optimal attitude control design that uses the Euler angles and angular velocities feedback is presented for regulation of spacecraft with disturbances. In the control design, it is assumed that the disturbance signal has the information of the system state. In addition, it is assumed that the disturbance signal tries to maximise the same performance index that the control input tries to minimise. After proposing a robust attitude control law that can stabilise the complete attitude motion of spacecraft with disturbances, the optimal attitude control problem of spacecraft is formulated as the optimal game-theoretic problem. Then it is shown that the proposed robust attitude control law is the optimal solution of the optimal game-theoretic problem. The stability of the closed-loop system for the proposed robust and optimal control law is proven by the LaSalle invariance principle. The theoretical results presented in this paper are illustrated by a numerical example.

Optimal attitude control for landing on asteroid with a flexible lander

The problem of the optimal control of a spacecraft reorientation from an arbitrary initial position into a prescribed final angular position is studied. For optimization, we use a generalized integral index characterizing the complexity of the rotation trajectory from the viewpoint of the "distance covered," which is the generalized rotation angle that takes into account the different weights of the spacecraft axes in the sense of expenditures (of fuel, time, or another irreplaceable resource) needed to rotate the spacecraft by the same angle. An analytical solution of this problem is obtained. Two versions of the optimal spacecraft slew maneuver problem (using the shortest trajectory) are considered--the quickest maneuver and a maneuver in the prescribed time. The optimal control problem is solved for several types of constraints on the control variables. The time of starting the deceleration is determined based on the actual motion parameters (mismatch angle and angular velocity) using the terminal control principles (based on the angular position and angular velocity measurements). An example and simulation results of the spacecraft dynamics under the optimal control are presented, which demonstrate the practical usefulness of the proposed control algorithms.

The problem of optimal control of a spacecraft reorientation from an arbitrary initial position into a prescribed final angular position is studied. The reorientation time is minimized. The case when the velocity parameters are limited is investigated. On the basis of necessary optimality conditions in the form of Pontryagin's maximum principle and using quaternion variables for the control problems of the spacecraft motion, an analytical solution of the stated problem is obtained. The kinematic problem of spacecraft reorientation is solved completely. Formal equations are derived and computational expressions for constructing the optimal control program are obtained. For the symmetric form of constraints on the angular velocity vector, the optimal reorientation problem is solved analytically (the result is obtained in terms of elementary functions). Results of the mathematical simulation of the spacecraft motion under the optimal control are presented that demonstrate the practical usefulness of the proposed algorithm for the spacecraft attitude control.

Attitude estimation of satellites using Kalman Filters has been in practice for many years. The optimal attitude control in the presence of noise can be achieved by using the optimal controller and the optimal estimator, simultaneously. In this paper, the Linear Quadratic Regulator (LQR) has been implemented in conjunction with the Extended Kalman Filter (EKF) on a CubeSat model. Full quaternion-based model (dynamics & kinematics) of the CubeSat is employed for the design of LQR. Furthermore, an extended Kalman filter is designed using the reduced quaternion model. The filter is then implemented in the closed loop with the LQR, and the simulations are conducted. The data generation using the full quaternion model and the filter implementation using the reduced model, provide the benefit of computational ease all the while catering for any singularities in the model. The simulation results show adequate attitude control, estimation and noise filtration within a reasonable time and optimum control effort.

In conventional DC microgrid control schemes, optimization and real-time control are usually performed at different time scales. It is hard for such control schemes to achieve real-time optimization. Even a small disturbance can result in deviations of bus voltages and output currents from their optimal operating points. In addition, most real-time controllers cannot guarantee the satisfaction of pre-defined constraints on individual bus voltages due to the disconnection between steady-state optimization and real-time control. In this paper, a distributed optimal control scheme is presented for DC microgrid. The objectives are to simultaneously realize generation cost minimization and individual bus voltage regulation. First, the optimal control problem is formulated, based on which a necessary and sufficient optimality condition is derived that characterizes the optimal operating points. The distributed optimal controller is then proposed to dynamically drive the system to operate at the optimality condition. Convergence to the optimal operating points that minimizes generation cost under constraints is guaranteed through rigorous Lyapunov synthesis. Each individual bus voltage can also be maintained within bounds in both transient- and steady-state. The performance of the proposed controller is validated through simulations based on a switch-level microgrid model.

In this paper, a coordinated optimal control is designed to simultaneously satisfy multiple power system objectives at the distribution network level. With high penetration of renewables, traditional generation and control may not be enough to compensate for intermittent changes in net load. Dynamic coordination of battery storage devices and demand response at aggregated distributed energy resource (DER) sites becomes necessary to maintain power system operation, however, each dynamic power component operates at different time scales. Frequency stabilization can be achieved by designing optimal controls for traditional generation, storage devices and demand response. The proposed optimal controls naturally render frequency separation of these load balancing mechanisms. Given a 24-hour net load forecast, optimal tracking control inputs are designed subject to constraints of selected system elements to ensure optimal performance of the power system. Simulation results are presented and discussed.