Niranjan Balachandran

Atreyee Kundu, Niranjan Balachandran, Debasish Chatterjee

In this article we study algorithmic synthesis of the class of stabilizing switching signals for discrete-time switched linear systems proposed in [12]. A weighted digraph is associated in a natural way to a switched system, and the switching signal is expressed as an infinite walk on this weighted digraph. We employ graph-theoretic tools and discuss different algorithms for designing walks whose corresponding switching signals satisfy the stabilizing switching conditions proposed in [12]. We also address the issue of how likely/generic it is for a family of systems to admit stabilizing switching signals, and under mild assumptions give sufficient conditions for the same. Our solutions have both deterministic and probabilistic flavours.

Priyanka Dey, Niranjan Balachandran, Debasish Chatterjee

This article studies two problems related to observability and efficient constrained sensor placement in linear time-invariant discrete-time systems with partial state observations. (i) We impose the condition that both the set of outputs and the state that each output can measure are pre-specified. We establish that for any fixed \(k > 2\), the problem of placing the minimum number of sensors/outputs required to ensure that the structural observability index is at most \(k\), is NP-complete. Conversely, we identify a subclass of systems whose structures are directed trees with self-loops at every state vertex, for which the problem can be solved in linear time. (ii) Assuming that the set of states that each given output can measure is given, we prove that the problem of selecting a pre-assigned number of sensors in order to maximize the number of states of the system that are structurally observable is also NP-hard. As an application, we identify suitable conditions on the system structure under which there exists an efficient greedy strategy, which we provide, to obtain a \((1-\frac{1}{e})\)-approximate solution. An illustration of the techniques developed for this problem is given on the benchmark IEEE 118-bus power network containing roughly \(400\) states in its linearized model.

Priyanka Dey, Niranjan Balachandran, Debasish Chatterjee

This article determines and characterizes the minimal number of actuators needed to ensure structural controllability of a linear system under structural alterations that can severe the connection between any two states. We assume that initially the system is structurally controllable with respect to a given set of controls, and propose an efficient system-synthesis mechanism to find the minimal number of additional actuators required for resilience of the system w.r.t such structural changes. The effectiveness of this approach is demonstrated by using standard IEEE power networks.