Finite-time differential games in missile guidance: Achieving motion camouflage and robust cooperative encirclement guidance.

In this paper, a robust differential game guidance law is proposed for the nonlinear zero-sum system with unknown dynamics and external disturbances. First, the continuous-time nonlinear zero-sum differential game problem is transformed into solving the nonlinear Hamilton–Jacobi–Isaacs equation, a time-varying cost function is developed to reflect the fixed terminal time, and the robust guidance law is developed to compensate for the external disturbance. Then, a novel neural network identifier is designed to approximate the unknown nonlinear dynamics with online weight tuning. Subsequently, an online critic neural network approximator is presented to estimate the cost function, and time-varying activation functions are considered to deal with the fixed final time problem. An adaptive weight tuning law is given, where two additional terms are added to ensure the stability of the closed-loop nonlinear system and so as to meet the terminal cost at a fixed final time. Furthermore, the uniform ultimate boundedness of the closed-loop system and the critic neural network weights estimation error are proven based upon the Lyapunov approach. Finally, some simulation results are presented to demonstrate the effectiveness of the proposed robust differential game guidance law for nonlinear interception.

Guidance strategy of motion camouflage for spacecraft pursuit-evasion game

Linear-quadratic and norm-bounded differential game combined guidance strategy against active defense aircraft in three-player engagement

We prove the existence of a value for pursuit games with state constraints. We also prove that this value is lower semicontinuous.

Observer-based robust impact angle control three-dimensional guidance laws with autopilot lag

In this paper, a new robust guidance law is designed to satisfy both impact angle constraint and the seeker’s field-of-view limit for missiles with strapdown seekers. Since the impact angle guidance law needs a highly curved trajectory and most strapdown seekers have a very narrow field-of-view, maintaining the seeker’s lock-on is the key issue for these missiles. To address this problem, a switching logic is adopted, which adds an additional term in the original guidance law when the look angle exceeds the pre-designed boundary value to maintain the seeker’s lock-on. An impact angle guidance law is designed based on terminal sliding mode control theory and the finite time convergence characteristic of the line-of-sight angle, as well as its derivative is proved through the Lyapunov method. Numerical simulations are performed to validate the effectiveness of the proposed guidance law. Some intuitive tunings of the design parameters are also offered in the simulation results to achieve large impact angles.

I. Zero-sum differential games: Theory and applications in worst-case controller design.- A Theory of Differential Games.- H?-Optimal Control of Singularly Perturbed Systems with Sampled-State Measurements.- New Results on Nonlinear H? Control Via Measurement Feedback.- Reentry Trajectory Optimization under Atmospheric Uncertainty as a Differential Game.- II. Zero-sum differential games: Pursuit-evasion games and numerical schemes.- Fully Discrete Schemes for the Value Function of Pursuit-Evasion Games.- Zero Sum Differential Games with Stopping Times: Some Results about its Numerical Resolution.- Singular Paths in Differential Games with Simple Motion.- The Circular Wall Pursuit.- III. Mathematical programming techniques.- Decomposition of Multi-Player Linear Programs.- Convergent Stepsizes for Constrained Min-Max Algorithms.- Algorithms for the Solution of a Large-Scale Single-Controller Stochastic Game.- IV. Stochastic games: Differential, sequential and Markov Games.- Stochastic Games with Average Cost Constraints.- Stationary Equilibria for Nonzero-Sum Average Payoff Ergodic Stochastic Games and General State Space.- Overtaking Equilibria for Switching Regulator and Tracking Games.- Monotonicity of Optimal Policies in a Zero Sum Game: A Flow Control Model.- V. Applications.- Capital Accumulation Subject to Pollution Control: A Differential Game with a Feedback Nash Equilibrium.- Coastal States and Distant Water Fleets Under Extended Jurisdiction: The Search for Optimal Incentive Schemes.- Stabilizing Management and Structural Development of Open-Access Fisheries.- The Non-Uniqueness of Markovian Strategy Equilibrium: The Case of Continuous Time Models for Non-Renewable Resources.- An Evolutionary Game Theory for Differential Equation Models with Reference to Ecosystem Management.- On Barter Contracts in Electricity Exchange.- Preventing Minority Disenfranchisement Through Dynamic Bayesian Reapportionment of Legislative Voting Power.- Learning by Doing and Technology Sharing in Asymmetric Duopolies.

A three-dimensional robust nonlinear cooperative guidance law is proposed to address the challenge of multiple missiles intercepting manoeuvering targets under stringent input constraints and thruster failure. The finite-time convergence theory is used to design a distributed nonlinear sliding mode guidance law, ensuring that the system converges in finite time, with the upper limit of convergence time related to the initial state. A nonlinear sliding surface is adopted to mitigate actuator saturation issues. Then, considering thruster failure, a robust cooperative guidance law is further introduced, ensuring mission completion through the reconstruction of the guidance law. The closed-loop system is proven to be stable using Lyapunov theory, and the influence of hyperparameters on the cooperative guidance law is analysed. Additionally, the results of numerical simulations and hardware-in-the-loop experiments demonstrate the effectiveness and robustness of the proposed algorithm in dealing with stringent input saturation and various disturbances.

Three dimensional impact angle constrained integrated guidance and control for missiles with input saturation and actuator failure

Three-dimensional fixed-time robust cooperative guidance law for simultaneous attack with impact angle constraint

Considering the background of effective optimization and improvement of air defense missile performance, a self-tunning robust guidance law considering the energy miss distance constraints is designed based on an iterative extremum seeking algorithm. A nominal optimal robust guidance law with energy and terminal miss distance constraints is designed firstly. Using the iterative extremum seeking algorithm to auto-tuning the feedback parameters of the nominal guidance law. Then, the Lyapunov equation is used to verify the global stability of the designed guidance law. Finally, Mathematical simulations show that the designed method has the characteristics of good practicability, high precision, and strong robustness.KeywordsIterative extremum seeking algorithmMulti-parameter auto-tuningRobust guidance law

In this paper, cooperative guidance strategies for the survival of cooperating team of two unmanned aerial vehicles (UAVs) against two attackers are proposed. The guidance schemes are designed under the assumptions that each UAV is being pursued by one attacker without cooperation with other attacker. The guidance schemes are designed to combat attackers guided either by proportional navigation (PN) or augmented PN guidance methodologies. The attackers are lured onto a collision course with each other such that intra-attacker interception is achieved before the target UAVs are captured. Sliding mode control techniques are employed to satisfy the sufficiency conditions for the survival within a finite time. Due to the nonlinear framework used for guidance design, the proposed strategies remain effective even for the engagements with large heading angle errors. Numerical simulations are presented to demonstrate the effectiveness of the proposed guidance strategies under various engagement geometries.

This paper presents an innovative control strategy, the Adaptive Fast Terminal Sliding Mode Control (AFTSMC), designed for the stability control of an inverted pendulum on a cart. The proposed controller aims to stabilize the system within a finite time, leveraging the advantages of fast terminal sliding mode techniques. The system’s dynamic model is employed to derive the controller, utilizing an adaptive approach to accommodate uncertainties and disturbances. Simulations are conducted to validate the proposed AFTSMC, comparing its performance with an Adaptive Sliding Mode Controller under various scenarios. The results demonstrate the efficacy of the AFTSMC in achieving stable and precise control, making it a promising solution for the challenging dynamics of inverted pendulum systems.

Robust guidance algorithm using only line-of-sight rate measurement is proposed for the interceptor with passive seeker. The initial relative distance, initial closing velocity and their error boundaries are employed to obtain their estimations according to the interceptor-target relative kinematics. A robust guidance law based on sliding mode control is formulated, in which the boundary of target maneuver is needed and the chattering phenomenon inevitably exists. In order to address the defects above, an estimation to the boundary of the target acceleration is proposed to improve the robust guidance law and the Lyapunov stability analysis is included. The main feature of the robust guidance algorithm is that it reduces the influence of the relative distance, the closing velocity and the target maneuver on the interception and enhances the effect of line-of-sight rate. With two worst conditions of initial measured distance and initial measured closing velocity, performances of the proposed guidance laws are verified via numerical simulations against different target maneuvers.

This note proposes a robust guidance synthesis based on the passivity approach. The method is applied to missiles whose flight control dynamics are modeled as linear uncertain systems with bounded uncertainties. The robust guidance laws are obtained by means of an appropriate subsystem decomposition, providing passivation by feedback and feedforward control. Hence, L/sub 2/ stability of the missile-target closed-loop system is warranted by direct application of the passivity theorem. The resulting terminal guidance laws ensure robust stability of the null miss distance in the case of 1) a maneuvering target whose acceleration lies in L/sub 2/, and 2) bounded parametric uncertainties of second-order models of the missile flight control dynamics. Numerical simulations demonstrate the effectiveness of the proposed guidance laws.