Methods and systems for the design and implementation of optimal multivariable model predictive controllers for fast-sampling constrained dynamic systems
View Patent ↗Methods and systems for the design and implementation of optimal multivariable MPC controllers for fast-sampling constrained dynamic systems utilizing a primal-dual feasibility approach and/or a graph approach. The primal-dual feasibility approach can compute and store matrices defining constraints of quadratic programming problems in an off-line part in order to calculate vectors of Lagrange multipliers and an optimizer. Then primal-dual feasibility can be checked in an on-line part using the Lagrange multipliers and the optimizer can provide a unique optimal solution for the constrained dynamic system. The graph approach can compute and store the matrices and the vectors, and also prepare and store a structure of directed graph in off-line part. An optimizer for a given parameter vector can be determined in on-line part using the directed graph, the matrices and the vectors.
1. A computer-implemented method for controlling a constrained dynamic system, said computer-implemented method comprising:
providing a state observer for determining a plurality of values associated with a constrained dynamic system in order to generate a plurality of state variables thereof; and
implementing an explicit quadratic programming solver having an off-line part and an on-line part, said explicit quadratic programming solver solving at least one explicit quadratic programming problem utilizing at least one of a primal-dual feasibility algorithm and a graph algorithm, wherein said explicit quadratic programming solver computes a plurality of control signals based on said plurality of state variables and a plurality of matrices stored in said off-line part of said explicit quadratic programming solver to control said constrained dynamic system.
2. The computer-implemented method of claim 1 wherein said on-line part utilizes said primal-dual feasibility algorithm and/or said graph algorithm.
3. The computer-implemented method of claim 1 wherein said off-line part solves a model predictive control problem and delivers with respect to said primal-dual feasibility algorithm, a data structure comprising vectors and matrices defining constraints related to the explicit quadratic programming problem.
4. The computer-implemented method of claim 1 wherein said off-line part solves a model predictive control problem and delivers with respect to said graph algorithm, a plurality of matrices, a plurality of vectors and a structure containing a directed graph.
5. The computer-implemented method of claim 1 wherein said plurality of values associated with said constrained dynamic system comprise a plurality of present and/or past values associated with at least one actuator and at least one sensor utilized in said constrained dynamic system.
6. The computer-implemented method of claim 5 further comprising associating said state observer with said at least one sensor and said at least one actuator.
7. The computer-implemented method of claim 1 wherein said primal-dual feasibility algorithm further comprises:
computing and storing said plurality of matrices in said off-line part of said explicit quadratic programming solver in order to calculate a plurality of vectors of Lagrange multipliers and an optimizer in said on-line part of said explicit quadratic programming solver; and
checking a primal-dual feasibility of said plurality of vectors in said on-line part of said explicit quadratic programming solver utilizing said Lagrange multipliers and said optimizer to determine a unique optimal solution for said constrained dynamic system.
8. The computer-implemented method of claim 1 wherein said graph algorithm further comprises:
computing and storing said plurality of matrices and said plurality of vectors, and constructing and storing a directed graph in said off-line part of said explicit quadratic programming solver, wherein said directed graph is associated with a plurality of control laws and a plurality of constraints;
determining a set of feasible control laws utilizing said directed graph; and
determining an optimal control law within said set of feasible control laws in said on-line part of said explicit quadratic programming solver.
9. The computer-implemented method of claim 8 wherein said plurality of matrices is defined for one or more feasible combinations of said plurality of constraints.
10. The computer-implemented method of claim 1 wherein said primal-dual feasibility algorithm and said graph algorithm are applicable in a model predictive control application and an embedded application having a low computing power, a low memory, and a fast sample time.
11. The computer-implemented method of claim 1 implemented by a multivariable controller that comprises a specialized real-time control platform.
12. The computer-implemented method of claim 11 wherein said specialized real-time control platform includes an electronic controller unit.
13. A computer-implemented method for controlling a constrained dynamic system, said computer-implemented method comprising:
providing a state observer for determining a plurality of values associated with a constrained dynamic system in order to generate a plurality of state variables thereof; and
implementing an explicit quadratic programming solver having an off-line part and an on-line part, said explicit quadratic programming solver solving at least one explicit quadratic programming problem utilizing at least one of a primal-dual feasibility algorithm and a graph algorithm, wherein said explicit quadratic programming solver computes a plurality of control signals based on said plurality of state variables and a plurality of matrices stored in said off-line part of said explicit quadratic programming solver to control said constrained dynamic system, and wherein said on-line part utilizes said primal-dual feasibility algorithm and/or said graph algorithm.
14. The computer-implemented method of claim 13 wherein:
said off-line part solves a model predictive control problem and delivers with respect to said primal-dual feasibility algorithm, a data structure comprising vectors and matrices defining constraints related to the explicit quadratic programming problem; or
wherein said off-line part solves a model predictive control problem and delivers with respect to said graph algorithm, a plurality of matrices, a plurality of vectors and a structure containing a directed graph.
15. A system for controlling a constrained dynamic system, comprising:
a processor;
a data bus coupled to said processor; and
a computer-usable medium embodying computer code, said computer-usable medium being coupled to said data bus, said computer program code comprising instructions executable by said processor and configured for:
providing a state observer for determining a plurality of values associated with a constrained dynamic system in order to generate a plurality of state variables thereof; and
implementing an explicit quadratic programming solver having an off-line part and an on-line part, said explicit quadratic programming solver solving at least one explicit quadratic programming problem utilizing at least one of a primal-dual feasibility algorithm and a graph algorithm, wherein said explicit quadratic programming solver computes a plurality of control signals based on said plurality of state variables and a plurality of matrices stored in said off-line part of said explicit quadratic programming solver to control said constrained dynamic system.
16. The system of claim 15 wherein said on-line part utilizes said primal-dual feasibility algorithm and/or said graph algorithm.
17. The system of claim 15 wherein said off-line part solves a model predictive control problem and delivers with respect to said primal-dual feasibility algorithm, a data structure comprising vectors and matrices defining constraints related to the explicit quadratic programming problem.
18. The system of claim 15 wherein said off-line part solves a model predictive control problem and delivers with respect to said graph algorithm, a plurality of matrices, a plurality of vectors and a structure containing a directed graph.
19. The system of claim 15 wherein said plurality of values associated with said constrained dynamic system comprise a plurality of present and /or past values associated with at least one actuator and at least one sensor utilized in said constrained dynamic system.
20. The system of claim 15 wherein said primal-dual feasibility algorithm further comprises:
computing and storing said plurality of matrices in said off-line part of said explicit quadratic programming solver in order to calculate a plurality of vectors of Lagrange multipliers and an optimizer in said on-line part of said explicit quadratic programming solver; and
checking a primal-dual feasibility of said plurality of vectors in said on-line part of said explicit quadratic programming solver utilizing said Lagrange multipliers and said optimizer to determine a unique optimal solution for said constrained dynamic system.