Control optimization objective

The use of a minimum schedule may, in some cases, result in a higher control cost when compared to a non-minimal schedule (minimal schedules were presented in Chapter 6). The topic of this chapter to find a schedule such that the control cost is minimized while still satisfying all of the consfiaints. 

---

Relative and absolute MIP gap mixed integer programming parameter for controlling optimization accuracy e g. MIP gap of 1% leads to an algorithm stop, if the objective value cannot be improved within a tolerance interval of 1%. 

Optimal Control. Optimal control is extension of the principles of parameter optimization to dynamic systems. In this case one wishes to optimize a scalar objective function, which may be a definite integral of some function of the state and control variables, subject to a constraint, namely a dynamic equation, such as Equation (1). The solution to this problem requires the use of time-varying Lagrange multipliers for a general objective function and state equation, an analytical solution is rarely forthcoming. However, a specific case of the optimal control problem does lend itself to analytical solution, namely a state equation described by Equation (1) and a quadratic objective function given by... 

Where fd is a factor (smaller than 1) used to compensate for rmit distrrrbances, and PNactcontr is the potential nrrmber of active controlled variables, which is defined according to the optimization objectives and the controller potential for effective action upon these variables. 

The description hierarchy acquires different ways physical processes in mass and energy balances information processing and control optimization of the system at the reactor level or as a whole (41). The most elaborate concept of descriptive hierarchy, including a set of programs, was published and routinely used by Klir (42). As descriptive hierarchy usually follows structural and functional hierarchy, it is thus assured that the modelled object possesses enough structural and functional features, otherwise the reactor control by means of such models would not satisfactorily respond to changing conditions. 

When solving an optimal control problem, it has to be kept in mind that several local optima may exist. Consider for example a problem with a single control function. The objective functional value may be locally optimal, i.e., optimal only in a vicinity of the obtained optimal control function. In another location within the space of all admissible control functions, the objective functional may again be locally optimal corresponding to some other optimal control function. This new optimal objective functional value may be better or worse than, or, even the same as the previous one. 

In most problems, a Lagrange multiplier can be shown to be related to the rate of change of the optimal objective functional with respect to the constraint value. This is an important result, which will be utilized in developing the necessary conditions for optimal control problems having inequality constraints. 

With initial controls, the constraint violation in terms of q was 55.7, which reduced and converged to 3.3x10 in 10 outer iterations. At convergence, the optimal objective functional was —4.45, which corresponds to the final product concentration of 4.45 g/cm. The optimal final time reduced from 60 to 33.3 min. 

To deal with the mentioned integration, this investigation proposes the uses of the BPM (Business Process Management) methodology, which aim is to improve the efficiency through the management of business process that are modelled, automatized, integrated, controlled and continuously optimized (Object... 

The minimum slack is the worst slack in a subcircuit. For two subcircuits with identical worst slack, it is possible that one subcircuit has few critical paths with worst slack while the other one has many. A timing optimization has to improve both the worst slack and the overall total threshold slack (TTS) in a subcircuit. TTS is defined as the sum of all slacks below a threshold. If the slack threshold is zero, TTS is equivalent to the total negative slack. With the minimum slack as the only objective, a small improvement in the worst slack may cause a large TTS degradation. Therefore we must add a TTS component to the optimization objective. The balance between the minimum slack and the TTS is controlled by a parameter Wf, which is set to a relatively small value because the worst slack objective is more important. 

A new method for selecting controlled variables (c) as linear combination of measurements (y) is proposed based on the idea of self-optimizing control. The objective is to find controlled variables, such that a constant setpoint policy leads to near optimal operation in the presence of low frequency disturbances d). We propose to combine as many measurements as there are unconstrained degrees of freedom (inputs, u) and major disturbances such that opi d) = 0. To illustrate the ideas a gas-lift allocation example is included. The example show that the method proposed here give controlled variables with good self-optimizing properties. 

S.2.2.2. Objective Functions for System Optimization and Open-Loop Optimal Control. The objective function for system optimization of batch granulation is ... 

Its objective is to select tiie best possible decision for a given set of circumstances without having to enumerate all of the possibilities and involves maximization or minimization as desired. In optimization decision variables are variables in the model which you have control over. Objective function is a fimction (mathematical model) that quantifies the quality of a solution in an optimization problem. Constraints must be considered, conditions that a solution to an optimization problem must satisfy and restrict decision variables are determined by defining relationships among them. It must be found the values of die decision variables that maximize (minimize) the objective function value, while staying widiin the constraints. The objective function and all constraints are linear functions (no squared terms, trigonometric functions, ratios of variables) of the deeision variables [59, 60]. 

Suppose that the chief control objective is to maximize a production rate while satisfying inequality constraints on the inputs and the outputs. Assume that the production rate can be adjusted via a flow control loop whose set point is denoted as u sp in the MPC control structure. Thus, the optimization objective is to maximize u sp, or equivalently, to minimize u sp- Consequently, the performance index in (20-68) becomes = u sp-This expression can be derived by setting all of the weighting factors equal to zero except for c, the first element of c. It is chosen to be = -1. 

---