In this paper, sliding-mode-control-based guidance laws to intercept stationary, constant-velocity, and maneuvering targets at a desired impact angle are proposed. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the missile's lateral acceleration to enforce terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. The conditions for capturability are also presented. In addition, by considering a three-degree-of-freedom linear-interceptor dynamic model and by following the procedure used to design a dynamic sliding-mode controller, the interceptor autopilot is designed as a simple static controller to track the lateral acceleration generated by the guidance law. Numerical simulation results are presented to validate the proposed guidance laws and the autopilot design for different initial engagement geometries and impact angles.

Sliding-Mode Guidance and Control for All-Aspect Interceptors with Terminal Angle Constraints

Convex optimization is a class of mathematical programming problems with polynomial complexity for which state-of-the-art, highly efficient numerical algorithms with predeterminable computational bounds exist. Computational efficiency and tractability in aerospace engineering, especially in guidance, navigation, and control (GN&C), are of paramount importance. With theoretical guarantees on solutions and computational efficiency, convex optimization lends itself as a very appealing tool. Coinciding the strong drive toward autonomous operations of aerospace vehicles, convex optimization has seen rapidly increasing utility in solving aerospace GN&C problems with the potential for onboard real-time applications. This paper attempts to provide an overview on the problems to date in aerospace guidance, path planning, and control where convex optimization has been applied. Various convexification techniques are reviewed that have been used to convexify the originally nonconvex aerospace problems. Discussions on how to ensure the validity of the convexification process are provided. Some related implementation issues will be introduced as well.

Survey of convex optimization for aerospace applications

A nonlinear suboptimal guidance law is presented in this paper for successful interception of ground targets by air-launched missiles and guided munitions. The main feature of this guidance law is that it accurately satisfies terminal impact angle constraints in both azimuth as well as elevation simultaneously. In addition, it is capable of hitting the target with high accuracy as well as minimizing the lateral acceleration demand. The guidance law is synthesized using recently developed model predictive static programming (MPSP). Performance of the proposed MPSP guidance is demonstrated using three-dimensional (3-D) nonlinear engagement dynamics by considering stationary, moving, and maneuvering targets. Effectiveness of the proposed guidance has also been verified by considering first. order autopilot lag as well as assuming inaccurate information about target maneuvers. Multiple munitions engagement results are presented as well. Moreover, comparison studies with respect to an augmented proportional navigation guidance (which does not impose impact angle constraints) as well as an explicit linear optimal guidance (which imposes the same impact angle constraints in 3-D) lead to the conclusion that the proposed MPSP guidance is superior to both. A large number of randomized simulation studies show that it also has a larger capture region.

Impact-Angle-Constrained Suboptimal Model Predictive Static Programming Guidance of Air-to-Ground Missiles

Nanostructured and traditional thermal barrier coatings have been prepared by atmospherical plasma spraying (APS) on NiCrAlY-coated superalloy substrates. Nanostructured thermal barrier coating has relatively longer lifetime than the common coating after cyclic testing at 1050, 1100 and 1150 °C. A transient thermal structural finite element solution was employed to analyze the stress distribution in the coatings. The reasons why the two kinds of the coatings have different lifetimes have been explored. The results indicate that the stresses ( S x ) within the nanostructured yttria stabilized zirconia (YSZ) ceramic layer in the axial ( x ) direction is about 67% that of the traditional YSZ. The stress ( S y ) in the radial ( y ) direction at the vicinity of the interface between the thermally grown oxide scale (TGO) and the YSZ topcoat at the edge of the sample is only about 73% that of the traditional YSZ. So it could be concluded that the decrease of the stress in the nanostructured ceramic layers is a fundamental reason, resulting in longer thermal cycling lifetime of the nanostructured thermal barrier coating.

Comparison of thermal cycling behavior of plasma-sprayed nanostructured and traditional thermal barrier coatings

Stochastic energy management of smart microgrid with intermittent renewable energy resources in electricity market

In this paper, the highly nonlinear planetary-entry optimal control problem is formulated as a sequence of convex problems to facilitate rapid solution. The nonconvex control constraint is avoided ...

Constrained Trajectory Optimization for Planetary Entry via Sequential Convex Programming

This paper presents a convex approach to the numerical solution of the minimum-fuel low-thrust orbit transfer problem. The main contribution is the transformation of the original nonlinear optimal control problem into a sequence of convex optimization problems. First, the control is decoupled from the states through a change of variables. Then, by introducing a lossless convexification technique, the control constraints are convexified, and the original problem is relaxed into a sequence of second-order cone programming problems. The resulting subproblems can be solved in real time by efficient interior-point methods. Finally, the effectiveness of the proposed methodology is demonstrated through numerical simulations of the three-dimensional minimum-fuel Earth-to-Mars low-thrust transfer problem.

Minimum-Fuel Low-Thrust Transfers for Spacecraft: A Convex Approach

Real-Time Optimal Control for Irregular Asteroid Landings Using Deep Neural Networks

Advanced entry guidance systems could potentially enable future vehicles to generate feasible/optimal flight trajectories onboard for the latest mission requirements and track the new trajectories ...

Autonomous Entry Guidance for Hypersonic Vehicles by Convex Optimization

This study is motivated by the requirement of on-board trajectory optimization with guaranteed convergence and real-time performance for optimal spacecraft orbit transfers. To this end, a real-time optimal control approach is proposed using deep learning technologies to obtain minimum-time trajectories of solar sail spacecraft for orbit transfer missions. First, the minimum-time two-dimensional orbit transfer problem is solved by an indirect method, and the costate normalization technique is introduced to increase the probability of finding the optimal solutions. Second, by making novel use of deep learning technologies, three deep neural networks are designed and trained offline by the obtained optimal solutions to generate the guidance commands in real time during flight. Consequently, the long-standing difficulty of on-board trajectory generation is resolved. Then, an interactive network training strategy is presented to increase the success rate of finding optima by supplying good initial guesses for the indirect method. Moreover, a multiscale network cooperation strategy is designed to deal with the recognition deficiency of deep neural networks (DNNs) with small input values, which helps achieve highly precise control of terminal orbit insertion. Numerical simulations are given to substantiate the efficiency of these techniques, and illustrate the effectiveness and robustness of the proposed DNN-based trajectory control for future on-board applications.

Zhenbo Wang

Papers

Constrained Trajectory Optimization for Planetary Entry via Sequential Convex Programming

Minimum-Fuel Low-Thrust Transfers for Spacecraft: A Convex Approach

Real-Time Optimal Control for Irregular Asteroid Landings Using Deep Neural Networks

Autonomous Entry Guidance for Hypersonic Vehicles by Convex Optimization

Real-Time Optimal Control for Spacecraft Orbit Transfer via Multiscale Deep Neural Networks