By Daniel Axehill.

ISBN-10: 9185457906

ISBN-13: 9789185457908

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**Additional info for Applications of integer quadratic programming in control and communication**

**Example text**

5). Independently of the formulation chosen, the optimization problem can be solved as a Mixed Integer Quadratic Programming (MIQP) problem, [16]. As in linear MPC, the algorithm is implemented in a receding horizon fashion. The difference is that it is much more complicated to find the optimal control signal sequence, since the system is neither linear nor smooth, [16]. One way of reducing the computational complexity is to use tailored MIQP solvers. 3. The control law found is in the literature sometimes referred to as a Mixed Integer Predictive Control (MIPC) law, [16].

In [5], an Adaptive Cruise Control (ACC) problem for heavy vehicles is studied. In the reference, an MPC controller is used to control the distance to the vehicle in front of the ACC equipped vehicle. The main difficulty in the problem is to prohibit simultaneous use of throttle and brakes. This condition can easily be formulated by introducing a mixed integer linear inequality, which is a linear inequality involving real and binary variables. 2 Mixed Logical Dynamical Systems 37 hatches. 7) denotes the state of the system, partitioned into continuous states xc (t) and logical (binary) states xb (t).

Lagrange multipliers for inequality constraints not in the working set, are set to zero. 20c) is If there exists an index j ∈ Wk ∩ I such that λ not fulfilled and the objective function value can be decreased by dropping constraint j from the working set. This conclusion can be drawn from sensitivity analysis. If there exist negative multipliers, the index corresponding to one of them is removed from the working set and a new subproblem with this constraint removed is solved. In [77], it is shown that this strategy generates a search direction in the next subproblem that is feasible with respect to the dropped inequality constraint.

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