Modern Predictive Control explains how MPC differs from other control methods in its implementation of a control action. Most importantly, MPC provides the flexibility to act while optimizing—which is essential to the solution of many engineering problems in complex plants, where exact modeling is impossible.
The superiority of MPC is in its numerical solution. Usually, MPC is employed to solve a finite-horizon optimal control problem at each sampling instant and obtain control actions for both the present time and a future period. However, only the current control move is applied to the plant.
This complete, step-by-step exploration of various approaches to MPC:
- Introduces basic concepts of systems, modeling, and predictive control, detailing development from classical MPC to synthesis approaches
- Explores use of Model Algorithmic Control (MAC), Dynamic Matrix Control (DMC), Generalized Predictive Control (GPC), and Two-Step Model Predictive Control
- Identifies important general approaches to synthesis
- Discusses open-loop and closed-loop optimization in synthesis approaches
- Covers output feedback synthesis approaches with and without a finite switching horizon
This book gives researchers a variety of models for use with one- and two-step control. The author clearly explains the variations between predictive control methods—and the root of these differences—to illustrate that there is no one ideal MPC and that one should remain open to selecting the best possible model in each unique circumstance.
Systems, modeling and model predictive control
Systems
Modeling
State space model and input/output model
Discretization of continuous-time systems
Model predictive control (MPC) and its basic properties
Three typical optimal control problems of MPC
Finite-horizon control: an example based on "three principles"
Infinite-horizon control: an example of dual-mode suboptimal control
Development from classical MPC to synthesis approaches
Model algorithmic control (MAC)
Principle of MAC
Constraint handling
The usual pattern for implementation of MPC
Dynamic matrix control (DMC)
Step response model and its identification
Principle of DMC
Constraint handling
Generalized predictive control (GPC)
Principle of GPC
Some basic properties
Stability results not related to the concrete model coefficients
Cases of multivariable systems and constrained systems
GPC with terminal equality constraint
Two-step model predictive control
Two-step GPC
Stability of two-step GPC
Region of attraction by using two-step GPC
Two-step state feedback MPC (TSMPC)
Stability of TSMPC
Design of the region of attraction of TSMPC based on semiglobal stability
Two-step output feedback model predictive control (TSOFMPC)
Stability of TSOFMPC
TSOFMPC: case where the intermediate variable is available
Sketch of synthesis approaches of MPC
General idea: case discrete-time systems
General idea: case continuous-time systems
Realizations
General idea: case uncertain systems (robust MPC)
Robust MPC based on closed-loop optimization
A concrete realization: case continuous-time nominal systems
State feedback synthesis approaches
System with polytopic description, linear matrix inequality
On-line approach based on min-max performance cost: case zero-horizon
Off-line approach based on min-max performance cost: case zero-horizon
Off-line approach based on min-max performance cost: case varying-horizon
Off-line approach based on nominal performance cost: case zero-horizon
Off-line approach based on nominal performance cost: case varying-horizon
Synthesis approaches with finite switching horizon
Standard approach for nominal systems
Optimal solution to infinite-horizon constrained linear quadratic control utilizing synthesis approach of MPC
On-line approach for nominal systems
Quasi-optimal solution to the infinite-horizon constrained linear time-varying quadratic regulation utilizing synthesis approach of MPC
On-line approach for systems with polytopic description
Parameter-dependent on-line approach for systems with polytopic description
Open-loop optimization and closed-loop optimization in synthesis approaches
A simple approach based on partial closed-loop optimization
Triple-mode approach
Mixed approach
Approach based on single-valued open-loop optimization and its deficiencies
Approach based on parameter-dependent open-loop optimization and its properties
Approach with unit switching horizon
Output feedback synthesis approaches
Optimization problem: case systems with input-output (I/O) nonlinearities
Conditions for stability and feasibility: case systems with I/O nonlinearities
Realization algorithm: case systems with I/O nonlinearities
Optimization problem: case systems with polytopic description
Optimality, invariance and constraint handling: case systems with polytopic description
Realization algorithm: case systems with polytopic description
Bibliography
Index
Biography
Ding Baocang