Conventional objective functions employed in the paper are Integral of Time multiplied by Squared Error (ITSE) and Integral of Squared Error (ISE).
The controllers have fixed structure and theirs coefficients are selected using the performance indices: the settling time and integral performance index ITAE (the integral of time multiplied by absolute error).
For the integral of time multiplied by absolute error (ITAE) reference model tracking, a chain observer is designed to establish the virtual estimated states for the decoupled subsystems by utilizing the obtained approximated continuous-time models.
The problem of FOPID-PSS design is transformed as an optimization problem based on performance indices (PI), including Integral Absolute Error (IAE), Integral Squared Error (ISE), Integral of the Time-Weighted Absolute Error (ITAE) and Integral of Time multiplied by the Squared Error (ITSE), where, BA is employed to obtain the optimal stabilizer parameters.
These performance indices used to optimize the errors of the system are: mean of the squared error (MSE), integral of time multiplied by absolute error (ITAE), integral of absolute magnitude of the error (IAE), integral of the squared error (ISE), and time multiplied by the squared error (ITSE) to minimize the error signals and compare them to find the most suitable one [23].
The deterministic performance was evaluated through the integral of time multiplied by the absolute error (ITAE) and the quadratic variation of the control action; the stochastic performance was analyzed based on the normalized Harris index and on the variability and quadratic variation of the control actions.
Parameters of the lines are selected optimally in the sense of two criteria, i.e. integral absolute error (IAE) and integral of the time multiplied by the absolute error (ITAE).
The plane parameters (determining angles of inclination and the velocity of its motion) are selected to ensure the minimum integral of the time multiplied by the absolute error (ITAE) without violating velocity and input signal constraints.
The concentrations of metabolites and excreted molecules can be described using the integral of the time dependence of the corresponding precursor concentration, multiplied by the respective rate parameter.
Concerning the output (67), two cases have been taken into account: a distributed (in time) output - corresponding to h ( t ) = 1 - given by the integral of the temperature in time and space, and a concentrated (in time) output - corresponding to h ( t ) = δ ( t ) - given by the spatial integral of temperature at each timestep.
