Model Predictive Static Programming Research Articles

Constrained fault-tolerant control for hypersonic vehicle subject to actuator failure and with unmeasurable states

In this article, a novel constrained fault-tolerant control (FTC) scheme is proposed to solve the attitude tracking control problem of the hypersonic vehicle (HSV) subject to multiple constraints, actuator faults, and disturbances. The reentry model of HSV with state constraints and the fault model of aerodynamic surface considering surface deflection constraints are constructed firstly. The adaptive robust unscented Kalman filter (ARUKF)-based estimation algorithm is designed, which can quickly estimate state variables, stuck faults, partial loss of effectiveness (PLOE) faults, and disturbances at the same time. By utilising the improved model predictive static programming (MPSP) technique, the complexity of processing multiple constraints and the computation are significantly reduced. Moreover, the closed-loop control system stability of HSV is analysed and the simulation results under two fault cases are given to demonstrate the effectiveness of the presented FTC scheme.

Ascent Trajectory Optimization for Air-Breathing Hypersonic Vehicles Based on IGS-MPSP

This paper proposes an improved Generalized Quasi-Spectral Model Predictive Static Programming (GS-MPSP) algorithm for the ascent trajectory optimization for hypersonic vehicles in a complex flight environment. The proposed method guarantees the satisfaction of constraints related to the state and control vector while retaining its high computational efficiency. The spectral representation technique is used to describe the control variables, which reduces the number of decision variables and makes the control input smooth enough. Through Taylor expansion, the constraints are transformed into an inequality containing only decision variables, such that it can be added into GS-MPSP framework. By Gauss quadrature collocation method, only a few collocation points are needed to solve the sensitivity matrix, which greatly accelerates the calculation. Subsequently, the analytical expression is obtained by combining the static optimization with the penalty function method. Finally, the simulation results demonstrate that the proposed improved GS-MPSP algorithm can achieve both high computational efficiency and high terminal precision under the constraints.

Unspecified final-time nonlinear suboptimal guidance of aerobatic aircraft in air race

This paper presents a new suboptimal nonlinear guidance design for aerobatic aircraft in air race. This guidance design needs to ensure several stringent terminal conditions at the specified race gates, and to satisfy various path inequality constraints dependent on state and input throughout the flight trajectory such as bounds on control, altitude, velocity as well as structural load factor limits. It also requires to be robust in presence of uncertainties in aerodynamic parameters as well as external disturbances due to wind gust, which makes this guidance design more challenging. To meet these demanding requirements, the guidance commands are generated using an innovative extension of the generalized model predictive static programming (G-MPSP) technique for incorporating both state and input inequality constraints in unspecified final time framework. This formulation readjusts final time depending on online performance of the system. In addition, to ensure various state and input inequality bounds throughout the trajectory, a penalty function approach is followed with this unspecified final time G-MPSP formulation. The effectiveness of this guidance design approach is validated in an air race scenario, while comparing with the Chebyshev pseudospectral method. Simulation results by considering a large number of simulations indicate that the proposed approach is successful under parameter uncertainties and disturbances, demonstrating its robustness aspect.

Parallel-Structured Newton-Type Guidance by Using Modified Chebyshev–Picard Iteration

This paper presents a parallel-structured Newton-type guidance law for the missile guidance problems. In the proposed approach, the modified Chebyshev–Picard iteration is used to approximate the dynamic equations, by which the continuous-time guidance problem is transcribed into a sequence of discrete-time subproblems, and both serial and parallel computing can be supported. The subproblems can then be iteratively solved by the Newton-type methods. Numerical demonstrations in a 3-D air-to-surface missile guidance problem with both impact-time and impact-angle constraints are provided to illustrate the effectiveness of the proposed guidance law. The simulation results show that the proposed guidance is superior to the state-of-the-art adaptive damped Newton-type guidance and quasi-spectral model predictive static programming in both computational efficiency and accuracy, even before parallel implementation.

Constrained Quasi-Spectral MPSP With Application to High-Precision Missile Guidance With Path Constraints

Abstract This paper extends the recently developed quasi-spectral model predictive static programming (QS-MPSP) to include state and control path-constraints and yet retain its computational efficiency. This is achieved by (i) formulating the entire problem in the control variables alone by (a) converting the system dynamics to an equivalent algebraic constraint and (b) converting the state constraints to equivalent control constraints, both of which is done by manipulating the system dynamics, (ii) representing the control variables in Quasi-spectral form, which makes the number of free-variables independent of time-grids and (iii) using a computationally efficient optimization algorithm to solve this low-dimensional problem. This generic computationally efficient technique is utilized next as an effective lead angle, and lateral acceleration constrained optimal missile guidance to intercept incoming high-speed ballistic targets with high precision successfully. Both of these constraints, as well as near-zero miss-distance, are of high practical significance for this challenging problem. Extensive three-dimensional simulation studies show the effectiveness of the newly proposed constrained QS-MPSP guidance algorithm. Six degrees-of-freedom simulation studies have also been carried out using autopilot in the loop to validate the results more realistically.

Generalized quasi-spectral model predictive static programming method using Gaussian quadrature collocation

A new generalized quasi-spectral model predictive static programming (GS-MPSP) method is proposed to efficiently solve a class of terminal-constrained optimal control problems with specified or free terminal time. A spectral representation method is used to model the profile of the control vector, then an infinite-dimensional optimization problem in a continuous-time framework is transformed into a small-dimensional static programming problem minimizing a certain performance index. Using the Gauss quadrature collocation method, the computation of the sensitivity matrix can be converted to the solution of a group of linear equations and algebraic summation at a few collocation nodes. Subsequently, the spectral coefficients and terminal time are efficiently obtained to eliminate terminal output deviations by solving the static programming problem. A simulation case with a scenario of intercepting a high-speed target with a specified impact angle in the midcourse phase was conducted. The results indicate that the proposed GS-MPSP approach has increased computational efficiency compared to traditional methods.

Robust Bang-Off-Bang Low-Thrust Guidance Using Model Predictive Static Programming

Model Predictive Static Programming (MPSP) has been always used under the assumption of continuous or impulsive control, but never in low-thrust transfers featuring bang-off-bang control. Following the observation that the sensitivity matrix (SM) is discontinuous across the switching time, this work introduces a two-loop MPSP guidance scheme using fuel-optimal trajectories as nominal solutions. In our method, the equations of motion are augmented by the mass costate equation, while the velocity costate is the MPSP control, expressed by a weighted sum of Fourier basis functions. The SM is computed at the switching time by using calculus of variations. Both the MPSP control and the initial mass costate are updated in an inner loop using Newton’s method, and continuation is employed in an outer loop to face large perturbations. A sample interplanetary CubeSat mission to an asteroid is used as study case to illustrate the effectiveness and robustness of the method developed.

Suboptimal midcourse guidance design using generalized model predictive spread control

A new generalized model predictive spread control technique is presented for the midcourse guidance of interceptors that are designed to intercept high-speed ballistic missile targets. Because of using the basis functions, this new technique is further computationally efficient over the model predictive static programming technique. Also, the smoothness of the control variable is guaranteed for the smooth basis functions. For demonstrating the performance of the proposed technique, an interceptor midcourse guidance problem with an angle constraint is formulated and solved to intercept an incoming ballistic missile target successfully. Additionally, the results are compared with those of the midcourse guidance design using the model predictive static programming technique. A comparative study of the new technique has also been conducted with the quasi-spectral model predictive static programming technique proposed earlier in the literature. It has been observed that the orthogonality of the basis functions is a necessary assumption and without that, the quasi-spectral model predictive static programming technique is not a near-optimal technique. By using the new technique based on Legendre basis functions, the solution converges to the model predictive static programming method solution by increasing the number of basis functions with less computational load.

Multi-phase MPSP Guidance for Lunar Soft Landing

In this paper, an autonomous optimal guidance algorithm for multi-phase lunar soft landing is presented. Various stringent requirements of a typical multi-phase soft landing are incorporated in guidance formulation. The proposed guidance law is formulated using the model predictive static programming (MPSP), which is an emerging computational guidance algorithm. High accuracy on the terminal position and velocity at the end of each phase is ensured, as the formulation of the MPSP inherently poses terminal output as a set of hard constraints. The spacecraft terminal orientation requirement is embedded in the guidance formulation in a soft constrained manner. Moreover, to facilitate a smooth transition between successive segments, an initial continuity of the guidance command is also attempted in an approximate manner. The effectiveness of the proposed method is demonstrated with simulation results. A processor-in-loop simulation study has been presented to demonstrate the feasibility of the proposed guidance law for possible on-board implementation.

Smooth Interpolation-Based Fixed-Final-Time Command Generation

This paper proposes a command generation approach based on the smooth interpolation without twist constraints and the input–output relation developed by the generalized model predictive static programming. Commands are efficiently generated to achieve the desired terminal condition at a specified final time in an interpolative manner featuring a noniterative nature. The effectiveness of this approach is demonstrated through three different simulation studies including a double integrator benchmark, a soft lunar landing problem, and a cluster missile guidance problem.

Adaptive trajectory generation based on real-time estimated parameters for impaired aircraft landing

ABSTRACTThis paper is motivated by a need to address the challenge of securing a safe landing after suffering from inflight impairment. In this paper, a new adaptive generalised model predictive static programming (G-MPSP) is developed to generate a safe emergency landing trajectory for impaired aircraft. Utilising the computationally efficient G-MPSP framework, the proposed algorithm enables adaptation of model parameters based on the prediction errors to ensure reasonable guidance performance. Based on the estimated parameters, a feasible landing trajectory is then generated by the flexible finite-horizon G-MPSP with input constraints. The integrated approach features explicit closed-form solutions for both parameter estimation and trajectory generation. Its effectiveness is demonstrated by simulations in the presence of parameter uncertainties and noises and by comparison studies with the non-adaptive G-MPSP.

Suboptimal Midcourse Guidance with Terminal-Angle Constraint for Hypersonic Target Interception

For the problem of hypersonic target interception, a novel midcourse guidance method with terminal-angle constraint is proposed. Referring to the air-breathing and the boost-gliding hypersonic targets, flight characteristics and difficulties of interception are analyzed, respectively. The requirements of midcourse guidance for interceptors are provided additionally. The kinematics model of adversaries is established concerning line-of-sight coupling in longitudinal and lateral planes. Suboptimal guidance law with terminal-angle constraint, specifically the final line-of-sight angle or impact angle, is presented by means of model predictive static programming. The trajectory is optimized and the load factor would finally converge after penalizing control sequence and output deviations. The realization of terminal angle is firstly verified with a constant speed target. A full interception scenario is further simulated focusing on a typical boost-gliding target, which flies along a skipping trajectory. Results show the success of providing handover conditions for intercepting hypersonic targets.

Waypoint Constrained Multi-Phase Optimal Guidance of Spacecraft for Soft Lunar Landing

A waypoint constrained multi-phase nonlinear optimal guidance scheme is presented in this paper for the soft landing of a spacecraft on the Lunar surface by using the recently developed computationally efficient Generalized Model Predictive Static Programming (G-MPSP). The proposed guidance ensures that the spacecraft passes through two waypoints, which is a strong requirement to facilitate proper landing site detection by the on-board camera for mission safety. Constraints that are required at the waypoints as well as at the terminal point include position, velocity, and attitude of the spacecraft. In addition to successfully meeting these hard constraints, the G-MPSP guidance also minimizes the fuel consumption, which is a very good advantage. An optimal final time selection procedure is also presented in this paper to facilitate minimization of fuel requirement to the best extent possible. Extensive simulation studies have been carried out with various perturbations to illustrate the effectiveness of the algorithm. Finally, processor-in-loop simulation has been carried out, which demonstrates the feasibility of on-board implementation of the proposed guidance.

Three-Dimensional Impact Time and Angle Control Guidance Based on MPSP

A new nonlinear guidance law for air-to-ground missile cooperation attacks is proposed in this paper. This guidance law enables missiles with different initial conditions to attack targets simultaneously, and it can also precisely satisfy the terminal impact angle conditions in both flight-path angle and heading angle. The guidance law is devised using the model predictive static programming (MPSP) method, and the control saturation constraint is incorporated in the MPSP algorithm. The first-order-lag acceleration of the missile is taken as the state variable to realize the convergence of the terminal acceleration to zero. Moreover, a collision avoidance strategy for three-dimensional missile cooperative flight is proposed. The simulation results show that the guidance law can make the missiles hit the target accurately at the same time with the ideal impact angles and can realize the control saturation constraints of the missiles. This can increase the attack effects and is significant for collaborative attacks.

Unscented MPSP for Optimal Control of a Class of Uncertain Nonlinear Dynamic Systems

A new computationally efficient nonlinear optimal control synthesis technique, named as unscented model predictive static programming (U-MPSP), is presented in this paper that is applicable to a class of problems with uncertainties in time-invariant system parameters and/or initial conditions. This new technique is a fusion of two recent ideas, namely MPSP and Riemann–Stieltjes optimal control problems. First, unscented transform is utilized to construct a low-dimensional finite number of deterministic problems. The philosophy of MPSP is utilized next so that the solution can be obtained in a computational efficient manner. The control solution not only ensures that the terminal constraint is met accurately with respect to the mean value, but it also ensures that the associated covariance matrix (i.e., the error ball) is minimized. Significance of U-MPSP has been demonstrated by successfully solving two benchmark problems, namely the Zermelo problem and inverted pendulum problem, which contain parametric and initial condition uncertainties.

Geometric control with model predictive static programming on [formula omitted

This paper proposes a geometric attitude control approach with the model predictive static programming (MPSP) for a rigid body modeled on the Lie group SO(3). The modeling scheme can avoid the defects of the singularity associated with Euler angles and the unwinding phenomenon associated with quaternion, and the MPSP technique features a high computational efficiency and is capable of achieving hard terminal constraints. In this paper, the MPSP is extended to the geometric control on SO(3), using the variational principle, the left-invariance principle of SO(3) and the topology structure of the Lie algebra space so(3). The desired attitude is considered as the hard terminal constraint and the energy consumption is optimized in the optimal control formulation of the MPSP. Moreover, the system disturbance and the measurement error of the states are taken into account in the online application of the MPSP. Simulation results of a spacecraft attitude control illustrate the effectiveness of the proposed method.

Model Predictive Static Programming for Optimal Command Tracking: A Fast Model Predictive Control Paradigm

Inspired by fast model predictive control (MPC), a new nonlinear optimal command tracking technique is presented in this paper, which is named as “Tracking-oriented Model Predictive Static Programming (T-MPSP).” Like MPC, a model-based prediction-correction approach is adopted. However, the entire problem is converted to a very low-dimensional “static programming” problem from which the control history update is computed in closed-form. Moreover, the necessary sensitivity matrices (which are the backbone of the algorithm) are computed recursively. These two salient features make the computational process highly efficient, thereby making it suitable for implementation in real time. A trajectory tracking problem of a two-wheel differential drive mobile robot is presented to validate and demonstrate the proposed philosophy. The simulation studies are very close to realistic scenario by incorporating disturbance input, parameter uncertainty, feedback sensor noise, time delays, state constraints, and control constraints. The algorithm has been implemented on a real hardware and the experimental validation corroborates the simulation results.

Suboptimal trajectory programming for unmanned aerial vehicles with dynamic obstacle avoidance

With regard to the dynamic obstacles current unmanned aerial vehicles encountered in practical applications, an integral suboptimal trajectory programming method was proposed. It tackled with multiple constraints simultaneously while guiding the unmanned aerial vehicle to execute autonomous avoidance maneuver. The kinetics of both unmanned aerial vehicle and dynamic obstacles were established with appropriate hypotheses. Then it was assumed that the unmanned aerial vehicle was faced with terminal constraints and control constraints in the whole duration. Meanwhile, the performance index was established as minimum control efforts. The initial trajectory was generated according to optimized model predictive static programming. Next, the slack variables were introduced to transform the inequality constraints arising from dynamic obstacle avoidance into equality constraints. In addition, sliding mode control theory was utilized to determine these slack variables' dynamics by designing the approaching law of sliding mode. Then the avoidance trajectory for single or multiple dynamic obstacles was developed by this combined method. At last, a further trajectory optimization was conducted by differential dynamic programming. Consequently, the integral problem was solved step by step and numerical simulations demonstrated that the integral method possessed high computational efficiency.

Cooperative near-space interceptor mid-course guidance law with terminal handover constraints

A cooperative problem in mid-course guidance phase is addressed in this paper. For providing suitable initial conditions of successful terminal salvo attack, a novel finite-time cooperative mid-course guidance law with terminal handover constraints is proposed. Firstly, a three-dimensional guidance model of mid-course is decoupled in a planar line-of-sight frame as a two-point boundary value problem. The terminal handover constraints which can guarantee an ideal zero effort terminal engagement are proposed and analyzed. Secondly, the design of the cooperative mid-course guidance law is separated into two stages. The acceleration commands along the line-of-sight direction are developed based on the finite-time average-consensus protocol and super-twisting algorithm in the first stage. In the second stage, the model predictive static programming method is adopted to solve the two-point boundary value problem in line-of-sight frame with a known final time from first stage. Furthermore, sliding mode control theory is used in combination with model predictive static programming method to satisfy terminal handover constraints with bounded perturbation. Finally, numerical simulations of two four-interceptor cooperative scenario are carried out to verify the validity of the proposed cooperative guidance law. The simulation results reflect that all the four interceptors can reach their own predictive interception points with specific approach angles simultaneously.

Designing a closed-loop guidance system to increase the accuracy of satellite-carrier boosters' landing point

A novel closed loop guidance method is provided in this paper to increase the accuracy of satellite-carrier boosters' landing point. The proposed method can be used in the first stage of flight vehicles that fly in atmosphere. In this case, solid motor propelled boosters would be able to more accurately land on the desired point. Moreover, in sub-optimal technique, the closed-loop guidance system would produce commands after booster separation, which guide second stage of satellite-carrier from initial conditions to the desired condition of orbit injection. In this method, sub-optimal integrated solution of control and guidance in closed-loop is developed. This sub-optimal technique named as Model Predictive Static Programming (MPSP) that is based on nonlinear optimal control theory and derived from combined philosophies of Model Predictive Control and Approximate Dynamic Programming; solves a class of finite horizon optimal control problems with terminal constraints. Furthermore because sensitivity matrices that are necessary for obtaining this solution can be computed recursively, this technique is computationally efficient and is appropriate for online implementation. In this paper, the dynamic equations of system are modeled in the presence of aerodynamic loading and the servo-mechanism dynamic. Moreover, by considering integrated guidance and control loops, a solution of the guidance and control system is proposed by three-degree of freedom spherical earth simulation model in atmosphere. Result show that proposed closed-loop guidance not only is able to remove aerodynamic and thrust modeling errors in first stage by flight data update that caused to more accurate of boosters' landing point, but also would still be able to guide second stage of satellite-carrier to the desired condition of placement in the orbit.