Parameter Identification of Discrete-time Linear Time-invariant Systems Using State and Input Data

Yusheng Wei 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.1

Parameter identification involves two fundamental problems, the problem of identifiability and the problem of designing identification algorithms without using knowledge about system parameters. It is well-known that certain initial conditions can destroy identifiability. To avoid problematic initial conditions, we propose the concept of identifiability regardless of the initial condition for deterministic discrete-time linear time-invariant systems. Analysis shows that such an identifiability notion is equivalent to controllability. Identification of controllable systems with state and input measurements is achieved by proposing an algebraic approach. We observe from system dynamics that system parameters are the solution to a set of linear equations. The solution is unique if a data matrix constructed by snapshots of system state and input is invertible. Under a one-step delayed linear state and input feedback law, the data matrix is invertible if and only if the initial input does not belong to a finite set. A one-step delayed input feedback law incurs input sequences that violate a well-known persistent excitation condition for parameter identification. The motivation to initiate an input that escapes the finite set facilitates the design of an iterative algorithm to identify system parameters in finite time. We have shown that parameter identification can be still achieved without satisfying a persistent excitation condition regarding input sequence design.

Optimization of Transient Stability Control Part-Ⅰ : For Cases with Identical Unstable Modes

Yusheng Xue,Wei Li,David John Hill 대한전기학회 2005 International Journal of Control, Automation, and Vol.3 No.2

Based on the stability margin provided by the EEAC, the unstable contingencies can be classified into sets according to their unstable modes. This two-part paper develops a globally optimal algorithm for transient stability control to coordinate preventive actions and emergency actions. In the first part, an algorithm is proposed for a set of contingencies having identical unstable modes. Instead of iterations between discrete emergency actions and continuous preventive actions, the algorithm straightforwardly searches for a globally optimal solution. The procedure includes assessing a set of insufficient emergency schemes identified by the EEAC; calculating the related preventive actions needed for stabilizing the system; and selecting the scheme with the minimum overall costs. Simulations on a Chinese power system highlight its excellent performance. The positive results obtained are explained by analogizing settlements for 0-1 knapsack problems using the multi-points greedy algorithm.

Optimization of Transient Stability Control Part-Ⅱ : For Cases with Different Unstable Modes

Yusheng Xue,Wei Li,David John Hill 대한전기학회 2005 International Journal of Control, Automation, and Vol.3 No.2

rt-I of this two-part paper develops an optimal algorithm for transient stability control to coordinate the preventive actions and emergency actions for a subset of contingencies with an identical unstable mode. In this portion, several subsets of contingencies having dissimilar unstable modes are dealt with. Preventive actions benefiting a subset of contingencies may go against the stability of others, thus coordination among the optimal schemes for individual subsets is necessary. The coordination can be achieved by replacing some preventive actions with contingency-specified emergency actions. It is formulated as a classical model of economic dispatch with stability constraints and stability control costs. Such an optimal algorithm is proposed based on the algorithm in Part-I of the paper and is verified by simulations on a Chinese power system.

Optimization of Transient Stability Control Part-II: For Cases with Different Unstable Modes

Xue Yusheng,Li Wei,Hill David John Institute of Control 2005 International Journal of Control, Automation, and Vol.3 No.S

Part-I of this two-part paper develops an optimal algorithm for transient stability control to coordinate the preventive actions and emergency actions for a subset of contingencies with an identical unstable mode. In this portion, several subsets of contingencies having dissimilar unstable modes are dealt with. Preventive actions benefiting a subset of contingencies may go against the stability of others, thus coordination among the optimal schemes for individual subsets is necessary. The coordination can be achieved by replacing some preventive actions with contingency-specified emergency actions. It is formulated as a classical model of economic dispatch with stability constraints and stability control costs. Such an optimal algorithm is proposed based on the algorithm in Part-I of the paper and is verified by simulations on a Chinese power system.

Optimization of Transient Stability Control Part-I: For Cases with Identical Unstable Modes

Xue Yusheng,Li Wei,Hill David John Institute of Control 2005 International Journal of Control, Automation, and Vol.3 No.S

Based on the stability margin provided by the EEAC, the unstable contingencies can be classified into sets according to their unstable modes. This two-part paper develops a globally optimal algorithm for transient stability control to coordinate preventive actions and emergency actions. In the first part, an algorithm is proposed for a set of contingencies having identical unstable modes. Instead of iterations between discrete emergency actions and continuous preventive actions, the algorithm straightforwardly searches for a globally optimal solution. The procedure includes assessing a set of insufficient emergency schemes identified by the EEAC; calculating the related preventive actions needed for stabilizing the system; and selecting the scheme with the minimum overall costs. Simulations on a Chinese power system highlight its excellent performance. The positive results obtained are explained by analogizing settlements for 0-1 knapsack problems using the multi-points greedy algorithm.

Distributed Optimization Algorithms on Structurally Balanced Signed Networks

Wen Du,Yusheng Wei,Mingjun Du 제어로봇시스템학회 2021 제어로봇시스템학회 국제학술대회 논문집 Vol.2021 No.10

In this paper, we consider the distributed optimization problem under structurally balanced signed graph. First, we convert the original distributed optimization problem into a conditional minimum problem under the condition that the graph is structurally balanced. Our goal is to find the saddle points of augmented Lagrange function. Inspired by the Lagrange multiplier method, we present our algorithms for both undirected graph and digraph, and show that our algorithms asymptotically converge to the global minimizer. Particularly, our algorithms for digraph can not only handle the weight balanced case but the weight unbalanced case. We show that the unsigned graph is a special case of our signed graph cases. Finally, theoretical results are illustrated by numerical simulations.

Event-triggering Signed-average Consensus Algorithms under Directed Signed Networks

Wen Du,Yusheng Wei,Shengli Fu 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.9

In this paper, we consider a signed-average consensus problem under signed networks in which the interactions between agents depicted by edges with positive and negative weights. In order to decrease communication and computation burden, two dynamic event-triggering procotols have been proposed under the signed network that is depicted by the signed digraph. We prove that signed-average consensus is reached exponentially when the signed digraph is structurally balanced and strongly connected; state stability is reached when the signed digraph is structurally unbalanced and strongly connected; and Zeno behavior is excluded. Besides, when the underlying topology is structurally balanced (structurally unbalanced, respectively), we show that static event-triggering laws, which also achieve signed-average consensus (state stability, respectively), are special cases of the dynamic eventtriggering laws. We also conclude that when all agents cooperate with each other, which implies that the underlying signed digraph collapses into an unsigned digraph, our algorithms still work. Finally, numerical examples are given to verify our theoretical results.