Model Predictive Static Programming Technique Research Articles

Optimal control of mineral processing plants using constrained model predictive static programming

The model predictive static programming (MPSP) technique, which is extended recently to incorporate applicable state and control constraints, operates on the philosophy of nonlinear model predictive control (NMPC). However, it reduces the problem into a lower-dimensional problem of control variables alone, thereby enhancing computational efficiency significantly. Because of this, problems with larger dimensions and/or increased complexity can be solved using MPSP without changing the computational infrastructure. In this paper, the MPSP technique with applicable constraints is applied to two challenging control problems in the mineral processing industry: (i) a single-stage grinding mill circuit model, and (ii) a four-cell flotation circuit model. The results are compared with a conventional nonlinear MPC approach. Comparison studies show that constrained MPSP executes much faster than constrained MPC with similar/improved performance. Therefore, it can be considered a potential optimal control candidate for mineral processing plants.

Mars Atmospheric Entry Guidance using MPSP with State and Control Constraints

An optimal Mars entry guidance scheme is presented in this paper using the Model Predictive Static Programming (MPSP) technique accounting for the applicable state and control constraints. The guidance scheme is designed to maximize the terminal parachute deployment altitude while applying minimum control effort and satisfying hard constraints on desired terminal conditions such as final velocity and downrange. The proposed guidance computes the optimal bank angle profile to shape the trajectory of the spacecraft. Path constraints on heat rate, dynamic pressure, aerodynamic load, and bounds on bank angle are considered to guide the vehicle safely through the martian atmosphere. Moreover, in order to generate practically realizable bank angle profiles, an additional constraint on the bank angle rate is also applied. Next, using the MPSP technique, the nonlinear constrained optimal control problem is converted into a static quadratic optimization problem with linear equality and inequality constraints to solve it in a computationally efficient manner. The concept of flexible final time MPSP is incorporated to update the final time in an optimal fashion. Numerical simulations illustrate the ability of the proposed method to solve the guidance problem efficiently while satisfying the path and terminal constraints within the desired accuracy.

Sub-optimal fixed-finite-horizon spacecraft configuration control on SE(3)

For achieving the desired configuration of spacecraft at the desired fixed time, a sub-optimal fixed-finite-horizon configuration control method on the Lie group SE(3) is developed based on the Model Predictive Static Programming (MPSP). The MPSP technique has been widely used to solve finite-horizon optimal control problems and is known for its high computational efficiency thanks to the closed-form solution, but it cannot be directly applied to systems on SE(3). The methodological innovation in this paper enables that the MPSP technique is extended to the geometric control on SE(3), using the variational principle, the left-invariant properties of Lie groups, and the topology structure of Lie algebra space. Moreover, the energy consumption, which is crucial for spacecraft operations, is considered as the objective function to be optimized in the optimal control formulation. The effectiveness of the designed sub-optimal control method is demonstrated through an online simulation under disturbances and state measurement errors.

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.

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 by a 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.

Energy-Insensitive Guidance of Solid Motor Propelled Long Range Flight Vehicles Using MPSP and Dynamic Inversion

A energy-insensitive explicit guidance design is proposed in this paper by appending newly-developed nonlinear model predictive static programming technique with dynamic inversion, which render a closed form solution of the necessary guidance command update. The closed form nature of the proposed optimal guidance scheme suppressed the computational difficulties, and facilitate real-time solution. The guidance law is successfully verified in a solid motor propelled long range flight vehicle, for which developing an effective guidance law is more difficult as compared to a liquid engine propelled vehicle, mainly because of the absence of thrust cutoff facility. The scheme guides the vehicle appropriately so that it completes the mission within a tight error bound assuming that the starting point of the second stage to be a deterministic point beyond the atmosphere. The simulation results demonstrate its ability to intercept the target, even with an uncertainty of greater than 10% in the burnout time.

A HYBRID ENERGY-INSENSITIVE EXPLICIT GUIDANCE SCHEME FOR LONG RANGE FLIGHT VEHICLES WITH SOLID MOTORS

Combining the newly developed nonlinear model predictive static programming technique with null range direction concept, a novel explicit energy-insensitive guidance design method is presented in this paper for long range flight vehicles, which leads to a closed form solution of the necessary guidance command update. Owing to the closed form nature, it does not lead to computational difficulties and the proposed optimal guidance algorithm can be implemented online. The guidance law is verified in a solid motor propelled long range flight vehicle, for which coming up with an effective guidance law is more difficult as compared to a liquid engine propelled vehicle (mainly because of the absence of thrust cutoff facility). Assuming the starting point of the second stage to be a deterministic point beyond the atmosphere, the scheme guides the vehicle properly so that it completes the mission within a tight error bound. The simulation results demonstrate its ability to intercept the target, even with an uncertainty of greater than 10% in burnout time.