Читать книгу Multi-parametric Optimization and Control - Efstratios N. Pistikopoulos - Страница 4

1 Chapter 1Figure 1.1 A schematic representation of a two‐dimensional polytope .Figure 1.2 A schematic representation of the differences between two polytop...Figure 1.3 A schematic representation of (a) strongly and (b) weakly redunda...

2 Chapter 2Figure 2.1 The difference between the solution of an LP and an mp‐LP problem...Figure 2.2 A schematic representation of the solution of the mp‐LP problem f...Figure 2.3 A schematic representation of the connected‐graph theorem, (a) fr...Figure 2.4 Primal and dual degeneracy in linear programming. In (a), primal ...

3 Chapter 3Figure 3.1 The difference between the solution of a QP and an mp‐QP problem ...Figure 3.2 A schematic representation of the solution of the mp‐QP problem f...Figure 3.3 A schematic representation of some of the differences between (a)...Figure 3.4 A schematic representation of the connected‐graph theorem, (a) fr...Figure 3.5 The solution to problem 3.14. In (a) the partitioning of the para...

4 Chapter 4Figure 4.1 A schematic representation between the different exploration stra...Figure 4.2 A schematic representation of the failure of the variable step‐si...Figure 4.3 A schematic representation of the branch‐and‐bound algorithm resu...

5 Chapter 5Figure 5.1 The interpretation of mp‐MILP problems as a combination of severa...Figure 5.2 The schematic representation of the example of a comparison proce...Figure 5.3 The detection of the intersection between two critical regions, Figure 5.4 The partitioning of into and based on Eq. (5.7).Figure 5.5 The solution of problem (5.16). In (a) the partitioning of the pa...

6 Chapter 6Figure 6.1 The interpretation of mp‐MIQP problems as a combination of severa...Figure 6.2 The schematic representation of the example of a comparison proce...Figure 6.3 The detection of the intersection between two critical regions, Figure 6.4 The difference in the partitioning of a critical region due to co...Figure 6.5 The schematic representation of the envelopes of solutions. In (a...Figure 6.6 The solution of problem (6.9). In (a) the partitioning of the par...

7 Chapter 7Figure 7.1 The general framework for the solution of mp‐MIQP problems.Figure 7.2 A schematic representation of the global optimization approach fo...Figure 7.3 A schematic example of a branch‐and‐bound tree.Figure 7.4 A schematic perspective on the different comparison procedures, w...

8 Chapter 8Figure 8.1 The problem statistics of the test sets “POP_mpLP1” and “POP_...Figure 8.2 The problem statistics of the test sets “POP_mpMILP1” and “PO...Figure 8.3 The structure of the graphical user interface (GUI) of POP.Figure 8.4 The performance of the geometrical, combinatorial, and connected‐...Figure 8.5 The analysis of the computational effort spent on different aspec...Figure 8.6 The analysis of the computational effort spent on different aspec...Figure 8.7 The performance of the decomposition algorithm for the different ...Figure 8.8 The analysis of the computational effort spent on different compa...Figure 8.9 The analysis of the computational effort spent on different compa...

9 Chapter 10Figure 10.1 The concept of the receding horizon. A set of manipulated inpu...Figure 10.2 The solution of the mp‐MPC example problem. (a) The partitioning...

10 Chapter 11Figure 11.1 The solution of the mp‐MPC example problem. Left: (a) The partit...Figure 11.2 Comparison of the feasible regions between (a) the hybrid mp‐MPC...Figure 11.3 The solution of the mp‐MPC with disturbance example problem. (a)...Figure 11.4 The solution of the mp‐MPC with disturbance example problem. (a)...Figure 11.5 Indicative snapshots of the solution of the explicit reference t...Figure 11.6 Indicative snapshots of the solution of the explicit reference t...

11 Chapter 12Figure 12.1 A step‐by‐step outline of the PAROC framework.Figure 12.2 An outline of the model approximation procedure typically used w...Figure 12.3 Software interactions for the implementation of the closed‐loop ...Figure 12.4 Software interactions for the implementation of the closed‐loop ...Figure 12.5 Graphical representation of the binary distillation column examp...Figure 12.6 Critical regions for the solution of the mp‐MHE problem of the b...Figure 12.7 Critical regions for the solution of the mp‐MPC problem of the b...Figure 12.8 Closed loop validation results. Both the mp‐MHE and mp‐MPC schem...Figure 12.9 Step response (a) and impulse response (b) of the tank approxima...Figure 12.10 Closed‐loop validation results for liquid volume set‐point trac...