Finite-time Convergent Guidance Laws With Multiple Terminal Constraints

The primary objective of terminal guidance is to produce a minimum miss distance between the missile and the target.In current guidance law design,however,some other terminal constraints,such as impact angle constraint,impact time constraint and impact velocity constraint,are also of paramount importance.As a result,the suboptimal State Dependent Riccati Equation(SDRE)control,optimal polynomial control,trajectory shaping and finite-time sliding mode control methods are studied to design multiple terminal constrained guidance laws in this dissertation to deal with air-to-ground attack,salvo attack,maneuvering target interception and hypersonic gliding vehicle guidance problems.The impact angle constrainted guidance problem of intercepting ground targets by air-launched missiles is first considered.Firstly,the SDRE approach is studied to derive the finite-time convergent guidance law.By employing a state weighting matrix,the time-to-go information is not required and high terminal accuracy can be ensured.To enlarge the available impact angle region,the guidance law is further modified by introducing the line-of-sight(LOS)information.Then,the focus is placed on the optimal polynomial guidance law with finite-time convergence.A polynomial function of the guidance command is first proposed and its optimality is guaranteed by specially designing the corresponding control coefficients.The analytical solutions of the system states are then obtained and they are further used to analyze the feasible sets of the guidance gains which meet the desired terminal constraints.Finally,to enhance the robustness of the guidance system,the finite-time sliding mode control based guidance law is studied.By analyzing the specific sliding mode,the principle of the guidance gain selection is presented,which also ensures some operational margin for the terminal guidance phase.To realize a salvo attack,the studies for impact time and angle constrained guidance problem are carried out.First of all,a finite-time time-varying sliding mode control(TVSMC)technique is applied to fulfill the terminal constraints,in which a specific time-varying sliding mode surface is constructed with two design coefficients,based on the nonlinear engagement dynamics.To improve the tolerance of initial heading errors and broaden the application,a new frame of reference is introduced.In addition,by the virtue of the global sliding mode characteristics of TVSMC,the analytical solutions of the system states are expressed for the prediction and off-line parameter selection.But this guidance law can not deal with control saturation.To solve this problem,a trajectory shaping based guidance technique is further investigated on the basis of the linearized system model.The feasible guidance coefficients are determined on-line by using the closed-loop solutions of the system states.As a result,the corresponding guidance law can be updated on-line,which guarantees the terminal constraints can be satisfied even in the presence of control saturation.For the cases of intercepting a high maneuvering target and guiding a hypersonic gliding vehicle against a ground target,the impact angle constrained guidance law and the impact angle and velocity constrained guidance law are studied respectively.Firstly,a truncation-function-based finite-time sliding mode control(TFBFTSMC)technique is presented for a class of second-order nonlinear uncertain system.Under the control law,the system states will converge to zero at the desired finite time.In addition,the design principle of the truncation function is illustrated,which demonstrate the design flexibility.Then,the TFBFTSMC technique is applied to design the impact angle constrained guidance law for intercepting maneuvering targets.By choosing a feasible truncation function,the associated guidance law is able to drive the LOS error and its derivative both to zero at the time of interception,which guarantees a minimum miss distance as well as a desired impact angle.To improve the tolerance of pointing errors,a switching guidance logic is introduced.By utilizing this guidance logic,an all-aspect interception can be achieved.Finally,the TFBFTSMC technique is applied to the terminal guidance problem of a hypersonic gliding vehicle.Two different truncation functions are selected to design the impact angle control guidance laws in the vertical plane and horizontal plane respectively.Moreover,the impact velocity constraint is also satisfied by adjusting the lateral flight trajectory.