Harshal B. Oza

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

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.

Generalized Model Predictive Static Programming and Angle-Constrained Guidance of Air-to-Ground Missiles

A new generalized model predictive static programming technique is presented for rapidly solving a class of finite-horizon nonlinear optimal control problems with hard terminal constraints. Two key features for its high computational efficiency include one-time backward integration of a small-dimensional weighting matrix dynamics, followed bya static optimization formulation that requires only a static Lagrange multiplier to update the control history. It turns out that under Euler integration and rectangular approximation of finite integrals it is equivalent to the existing model predictive static programming technique. In addition to the benchmark double integrator problem, usefulness of the proposed technique is demonstrated by solving a three-dimensional angle-constrained guidance problem for an air-to-ground missile, which demands that the missile must meet constraints on both azimuth and elevation angles at the impact point in addition to achieving near-zero miss distance, while minimizing the lateral acceleration demand throughout its flight path. Simulation studies include maneuvering ground targets along with a first-order autopilot lag. Comparison studies with classical augmented proportional navigation guidance and modern general explicit guidance lead to the conclusion that the proposed guidance is superior to both and has a larger capture region as well.

A Nonlinear Suboptimal Guidance Law with 3D Impact Angle Constraints for Ground Targets

Using the recently developed model predictive static programming (MPSP) technique, a suboptimal guidance law is presented in this paper considering the three-dimensional nonlinear engagement dynamics. The main feature of the guidance law is that it accurately satisfies terminal impact angle constraints in both azimuth as well as elevation, in addition to being capable of hitting the target with high accuracy. Moreover, it minimizes the control eort (i.e. the latax demand) throughout the engagement and hence leads to an optimal trajectory as well. The guidance law is primarily based on nonlinear optimal control theory and hence imbeds eective trajectory optimization concept into the guidance law. The performance of the proposed scheme is investigated using nonlinear simulation studies for stationary, moving and maneuvering ground targets, by considering both thrusted as well as unthrusted vehicles. Multiple munition engagement results are also presented to show the eectiveness of the proposed guidance scheme in such a scenario. A comparison plot for the Zero Eort Miss (ZEM) is also included, which reconfirms the superiority of the proposed optimal guidance over an augmented proportional navigation guidance available in the literature to engage maneuvering targets.

CONTINUOUS UNIFORM FINITE TIME STABILIZATION OF PLANAR CONTROLLABLE SYSTEMS

Continuous homogeneous controllers are utilized in a full state feedback setting for the uniform finite time stabilization of a perturbed double integrator in the presence of uniformly decaying piecewise continuous disturbances. Semiglobal strong

Original article: Finite time stabilization of a perturbed double integrator with unilateral constraints

\mathcal{C}^1

Settling Time Estimate for a Second Order Sliding Mode Controller: A Homogeneity Approach

Lyapunov functions are identified to establish uniform asymptotic stability of the closed-loop planar system. Uniform finite time stability is then proved by extending the homogeneity principle of discontinuous systems to the continuous case with uniformly decaying piecewise continuous nonhomogeneous disturbances. A finite upper bound on the settling time is also computed. The results extend the existing literature on homogeneity and finite time stability by both presenting uniform finite time stabilization and dealing with a broader class of nonhomogeneous disturbances for planar controllable systems while also proposing a new class of homogeneous continuous controllers.

Discrete time sliding mode control with application to magnetic levitation system

A discontinuous second order sliding mode (twisting) controller is utilized in a full state feedback setting for the finite time stabilization of a perturbed double integrator in the presence of both a unilateral constraint and uniformly bounded persisting disturbances. The unilateral constraint involves rigid body inelastic impacts causing jumps in one of the state variables. Firstly, a non-smooth state transformation is employed to transform the unilaterally constrained system into a jump-free system. The transformed system is shown to be a switched homogeneous system with negative homogeneity degree where the solutions are well-defined. Secondly, a non-smooth Lyapunov function is identified to establish uniform asymptotic stability of the transformed system. The global, uniform, finite time stability is then proved by utilizing the homogeneity principle of switched systems. The novelty lies in achieving finite time stabilization in the presence of jumps in one of the states without the need to analyze the Lyapunov function at the jump instants. The proposed results are of theoretical significance as they bridge non-smooth Lyapunov analysis, quasi-homogeneity and finite time stability for a class of impact mechanical systems.

Robust finite time stability and stabilisation: A survey of continuous and discontinuous paradigms

Abstract A novel homogeneity approach to obtain an upper bound on the settling time for a robust second order sliding mode controller is presented. The stability analysis is substantiated by a global non-smooth Lyapunov function. The proposed method is applied to the ‘twisting’ controller and is based on a combination of global exponential stability and global finite time stability of switched systems. The homogeneity regions are established and are graphically illustrated. Recommended tuning rules for the twisting controller are presented. The proposed framework does not depend on the differential inequality of the Lyapunov function and hence provides a new methodology for obtaining the upper bound on the settling time for exponentially stable homogeneous systems.

Continuous second order sliding mode based robust finite time tracking of a fully actuated biped robot

This paper presents an interesting application of magnetic levitation system using discrete sliding mode control. There is a limited literature available for sliding mode control as applied to magnetic levitation system. In this work a model of linearized magnetic levitation system having small magnetic disc and cylinder with light weight is considered. As a part of review PD control and full state feedback with pole placement and Kalman estimator are presented. A discrete sliding mode control with multi-rate output feedback is then investigated for the present application. To mitigate chattering, discrete time power rate reaching based algorithm is applied. Numerical result for nonlinear system is also shown. In all the cases, inherently unstable system is shown to exhibit stability and stable initial condition response compared to the uncompensated system.

The Immune System: A Variable Structure Control Perspective

The aim of this paper is to provide a survey of the tools for analysis and synthesis of finite time stable controllers. The paper analyses the literature in continuous and discontinuous finite time stabilisation in a unified way covering both the fundamentals as well as the latest techniques available in this non-linear control paradigm. The contribution of the paper lies in its exposition of the robustness properties that continuous and discontinuous controllers guarantee. Some open problems are identified which are relevant to both the theory and practice of finite time stabilisation.