Optimal sliding mode controllers for attitude tracking of spacecraft

This paper studies two optimal sliding mode control laws using integral sliding mode control (ISM) for some spacecraft attitude tracking problems. Integral sliding mode control combining the first order sliding mode and optimal control is applied to quaternion-based spacecraft attitude tracking manoeuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the state dependent Riccati equation (SDRE) and Control Lyapunov function (CLF) approaches are used to solve the infinite-time nonlinear optimal problem. The second method of Lyapunov is used to show that tracking is achieved globally. An example of multiaxial attitude tracking manoeuvres is presented and simulation results are included to verify the usefulness of these controllers

Streamlining of the state-dependent Riccati equation controller algorithm for an embedded implementation

In many practical control problems the dynamics of the plant to be controlled are nonlinear. However, in most cases the controller design is based on a linear approximation of the dynamics. One of the reasons for this is that, in general, nonlinear control design methods are difficult to apply to practical problems. The State Dependent Riccati Equation (SDRE) control approach is a relatively new practical approach to nonlinear control that has the simplicity of the classical Linear Quadratic control method. This approach has been recently applied to control experimental autonomous air vehicles with relative success. To make the SDRE approach practical in applications where the computational resources are limited and where the dynamic models are more complex it would be necessary to re-examine and streamline this control algorithm. The main objective of this work is to identify improvements that can be made to the implementation of the SDRE algorithm to improve its performance. This is accomplished by analyzing the structure of the algorithm and the underlying functions used to implement it. At the core of the SDRE algorithm is the solution, in real time, of an Algebraic Riccati Equation. The impact of the selection of a suitable algorithm to solve the Riccati Equation is analyzed. Three different algorithms were studied. Experimental results indicate that the Kleinman algorithm performs better than two other algorithms based on Newton’s method. This work also demonstrates that appropriately setting a maximum number of iterations for the Kleinman approach can improve the overall system performance without degrading accuracy significantly. Finally, a software implementation of the SDRE algorithm was developed and benchmarked to study the potential performance improvements of a hardware implementation. The test plant was an inverted pendulum simulation based on experimental hardware. Bottlenecks in the software implementation were identified and a possible hardware design to remove one such bottleneck was developed

Integrated Guidance and Control of Missiles with Θ-D Method

A new suboptimal control method is proposed in this study to effectively design an integrated guidance and control system for missiles. Optimal formulations allow designers to bring together concerns about guidance law performance and autopilot responses under one unified framework. They lead to a natural integration of these different functions. by modifying the appropriate cost functions, different responses, control saturations (autopilot related), miss distance (guidance related), etc., which are of primary concern to a missile system designer, can be easily studied. A new suboptimal control method, called the θ-D method, is employed to obtain an approximate closed-form solution to this nonlinear guidance problem based on approximations to the Hamilton-Jacobi-Bellman equation. Missile guidance law and autopilot design are formulated into a single unified state space framework. The cost function is chosen to reflect both guidance and control concerns. The ultimate control input is the missile fin deflections. A nonlinear six-degree-of-freedom (6-DOF) missile simulation is used to demonstrate the potential of this new integrated guidance and control approach

Gradient-augmented supervised learning of optimal feedback laws using state-dependent Riccati equations

A supervised learning approach for the solution of large-scale nonlinear stabilization problems is presented. A stabilizing feedback law is trained from a dataset generated from State-dependent Riccati Equation solvers. The training phase is enriched by the use of gradient information in the loss function, which is weighted through the use of hyperparameters. High-dimensional nonlinear stabilization tests demonstrate that real-time sequential large-scale Algebraic Riccati Equation solvers can be substituted by a suitably trained feedforward neural network

Data-driven initialization of deep learning solvers for Hamilton-Jacobi-Bellman PDEs

A deep learning approach for the approximation of the Hamilton-Jacobi-Bellman partial differential equation (HJB PDE) associated to the Nonlinear Quadratic Regulator (NLQR) problem. A state-dependent Riccati equation control law is first used to generate a gradient-augmented synthetic dataset for supervised learning. The resulting model becomes a warm start for the minimization of a loss function based on the residual of the HJB PDE. The combination of supervised learning and residual minimization avoids spurious solutions and mitigate the data inefficiency of a supervised learning-only approach. Numerical tests validate the different advantages of the proposed methodology.Comment: MTNS 202

Continuous control of lunar orbits via electric propulsion

To find definite answers for the presence of water on the poles of Moon, to facilitate selection of future lunar landing sites and aid in construction of architectural bases, to assist proper lunar resource utilization and to improve lunar gravity models there is a great interest and need for highly accurate, reliable and efficient lunar surface mapping and communication. This thesis is intended to aid in proper selection of orbits for future lunar missions by demonstrating the impact of using electric propulsion on the search space of feasible and useful lunar orbits. The requirements for future lunar mapping and communication are studied and possible options to meet them are investigated. Based on coverage analysis, a constellation of three satellites in high altitude, circular and polar geo-synchronous orbit is proposed to provide an improved lunar communications architecture compared to those previously recommended in literature. Low altitude, circular and polar Sun-synchronous orbits are found to be the best candidate to meet future lunar mapping needs. The feasibility of using electric propulsion for stationkeeping and providing the orbit plane rotation required by these lunar mapping and communication options is determined --Abstract, page iii

Supervised learning for kinetic consensus control

In this paper, how to successfully and efficiently condition a target population of agents towards consensus is discussed. To overcome the curse of dimensionality, the mean field formulation of the consensus control problem is considered. Although such formulation is designed to be independent of the number of agents, it is feasible to solve only for moderate intrinsic dimensions of the agents space. For this reason, the solution is approached by means of a Boltzmann procedure, i.e. quasi-invariant limit of controlled binary interactions as approximation of the mean field PDE. The need for an efficient solver for the binary interaction control problem motivates the use of a supervised learning approach to encode a binary feedback map to be sampled at a very high rate. A gradient augmented feedforward neural network for the Value function of the binary control problem is considered and compared with direct approximation of the feedback law

Analysis of the theta-D filter as applied to hit-to-kill interceptors and satellite orbit determination

When designing feedback control systems, there is often a need for estimation methods that provide system information that is not readily available via sensors placed within the system. In many cases a sensor that measures a particular system state either does not exist or is prohibitively expensive. In addition, all realistic systems contain some degree of nonlinearity. This thesis focuses on two such cases: missile guidance with bearings-only measurements and GPS satellite orbit determination. In each case, a new nonlinear filter, the [theta]-D method, is used and evaluated for its performance in providing the necessary estimation. To aid the filter in the bearings-only application, a guidance law is formulated that assists the filter in estimating the target location despite the lack of range measurement. An implementation procedure, called the Staggered Filter Concept, is also presented for implementing a continuous filter, such as the [theta]-D filter, with measurements taken at discrete intervals. This procedure is used to implement the orbit determination algorithm on the Missouri S&T Satellite Team M-SAT mission --Abstract, page iii