Let Pq(n) be the set of all Subspaces in the vector space F n q. There is a Subspace distance dS(U, V ) between any two Subspaces U and V. A Subspace code is also a subset of Pq(n). It is known that dS(U, V ) ≥ dH(ν(πU), ν(πV )), where π ∈ Sn, ν(U) denotes the pivot vector of E(U) and E(U) is the reduced row echelon form of the generator matrix of U. In this paper, we show that if E(U) and E(V ) have at most one non-zero entry in each rows and each columns then the equality holds. Moreover, we introduce the sets GU, V = {π ∈ Sn | dS(U, V ) = dH(ν(πU), ν(πV ))} for any U, V ∈ Pq(n) and examine them in the spaces P2(4), P2(5), P2(6) and P3(4). It is shown that the groups 1, Z2, Z2 × Z2, S3, S4 and 1, Z2, Z2 × Z2, S3, D8, S3 × Z2, S4, S5 appears between these sets in P2(4) and P2(5), respectively. Moreover, the groups 1, Z2, Z2 ×Z2, S3, D8, Z2 ×Z2 ×Z2, S3 ×Z2, D8 ×Z2, S4, S3 × S3, S4 × Z2, (S3 × S3): 2, S5, S6 and 1, Z2, Z2 × Z2, S3, D8, S4 appears between these sets in P2(6) and P3(4), respectively.

We give a general overview of the state-of-the-art in Subspace system identification methods. We have restricted ourselves to the most important ideas and developments since the methods appeared in the late eighties. First, the basis of linear Subspace identification are summarized. Different algorithms one finds in literature (Such as N4SID, MOESP, CVA) are discussed and put into a unifying framework. Further, a comparison between Subspace identification and prediction error methods is made on the basis of computational complexity and precision of methods by applying them to a glass tube manufacturing process.

Unfalsified Adaptive control (UAC) is a recently proposed robust adaptive control strategy. In this paper, the UAC principles and algorithms are reviewed and Multi-Model UAC is followed as an intermediate between UAC and multiple model control. Different approaches in UAC and MMUAC are studied. Also, Multi-Model Unfalsified Generalized predictive control (MMUGPC) is proposed, which is a new control design strategy in the UAC framework. For an uncertain system, by utilizing several generalized predictive controllers and discrete switching between them with unfalsified control, a new structure is proposed and appropriate equations are derived. Simulation results show the effectiveness of proposed Multi-Model Unfalsified Generalized predictive control.

predictive control is one of the effective methods to reduce the effect of time delay and data dropout in networked control systems. In the proposed predictive control method, the control data is predicted as long as it covers the time delay and data dropout in the network, and the estimation of state variables is performed using the Kalman filter. By sending a package containing the predicted control data to the actuator and selecting the appropriate control data, the desired control performance of the system can be achieved. In this paper, the networked control system is considered as a switching system with an arbitrary switching signal. A criterion for evaluating the stability of the closed-loop system with time delay and data dropout is presented based on the theory of switching systems. Time delay and data dropout are selected as switching parameters and a subset of switching dynamic systems is created in the discrete state space. By providing the Lyapunov function for all subsets and solving matrix inequalities, the stability of the system can be investigated. The simulation results show the effect of data dropout on the stability of the system by considering the time delay in the forward and feedback channels.

In this paper, two predictive control methods for dual output multilevel rectifier are compared. The investigated structure is a seven-level PUC rectifier, which was selected based on high reliability and low cost. Increasing the number of input voltage levels helps to reduce the amount of harmonics and consequently reduce the size of power filters. On the other hand, current conduction in this converter is performed continuously and the problems of current discontinuity such as complexity in analysis and the requirement to use large induction filters on the DC side are solved. First, the design is accomplished based on the FCS-MPC method and two different output voltages with ratios of 1 and 3 are obtained. Also, the control of output DC voltages and unity input power factor is well provided. Then, to achieve better stability, the MPC method based on Lyapunov theory has been utilized. In this method, the target variables are defined in the Lyapunov function and the cost function is derived from the same Lyapunov function. The advantages of this approach compared to the conventional MPC method are no need for gain adjustment, easier implementation and fewer sensors (the load current is estimated using the PUC7 rectifier mathematical model). The simulation of both FCS-MPC and predictive control based on Lyapunov method is carried out using Matlab/Simulink and the results of both methods are presented and compared with each other. Finally, it can be seen that in the Lyapunov-based method, the tracking of the reference current is smoother and with less fluctuations, and the seven-level rectifier voltage also has a more regular and sinusoidal waveform.

Model predictive controllers rely on dynamic model of the process, most often linear models obtained by system identification. The advantage of MPC is the fact that it allows the current timeslot to be optimized by keeping future timeslots in account. In this paper, the transient performance of MPC method against DTC with non linear Hysteresis based controllers is presented. Then a comparative performance in terms of torque and flux ripple are presented for PTC and DTC of three phase induction motor drive. In predictive control the control objectives are defined as cost function, which is to be minimized to have a greater flexibility to include constraints which results in low computational complexity compared to DTC scheme. simulation results of PTC and DTC in MATLAB/ SIMULINK are shown and compared. This comparison between is carried out by validating the feasibility of PTC and highlighting some important implementation issues.