Set Of Control States Research Articles

Fractional Proportional Linear Control Systems: A Geometric Perspective on Controllability and Observability

The paper presents a detailed analysis of control and observation of generalized Caputo proportional fractional time-invariant linear systems. The focus is on identifying controllable states and observable systems within the controllable subspace, null space, and unobservable subspace of the proposed system. The necessary conditions for the controllable subspace and the necessary and sufficient conditions for observability criteria are firmly established. The controllable subspace is treated geometrically as the set of controllable states, while the observable system is characterized by a zero unobservable subspace. The results are reinforced by examples and will immensely benefit future studies on fractional-order control systems.

The impact of Illinois’ comprehensive handheld phone ban on talking on handheld and handsfree cellphones while driving

Introduction: Distracted driving has been linked to multiple driving decrements and is responsible for thousands of motor-vehicle fatalities annually. Most U.S. states have enacted restrictions on cellphone use while driving, the strictest of which prohibit any manual operation of a cellphone while driving. Illinois enacted such a law in 2014. To better understand how this law affected cellphone behaviors while driving, associations between Illinois’ handheld phone ban and self-reported talking on handheld, handsfree, and any cellphone (handheld or handsfree) while driving were estimated. Methods: Data from annual administrations of the Traffic Safety Culture Index from 2012–2017 in Illinois and a set of control states were leveraged. The data were cast into a difference-in-differences (DID) modeling framework, which compared Illinois to control states in terms of pre- to post-intervention changes in the proportion of drivers who self-reported the three outcomes. Separate models for each outcome were fit, and additional models were fit to the subset of drivers who talk on cellphones while driving. Results: In Illinois, the pre- to post-intervention decrease in the drivers’ probability of self-reporting talking on a handheld phone was significantly more extreme than that of drivers in control states (DID estimate −0.22; 95% CI −0.31, −0.13). Among drivers who talk on cellphones while driving, those in Illinois exhibited a more extreme increase in the probability of talking on a handsfree phone while driving than those control states (DID estimate 0.13; 95% CI 0.03, 0.23). Conclusions: These results suggest that Illinois’ handheld phone ban reduced talking on handheld phones while driving among study participants. They also corroborate the hypothesis that the ban promoted substitution from handheld to handsfree phones among drivers who talk on the phone while driving. Practical Applications: These findings should encourage other states to enact comprehensive handheld phone bans to improve traffic safety.

Controllability and observability of multi-agent systems with general linear dynamics under switching topologies

This paper investigates controllability and observability of multi-agent systems, in which all the agents adopt identical general linear dynamics and the interconnection topologies are switching. For controllability, criteria are established by virtue of the switching sequence and the constructed subspace sequence, respectively. Furthermore, controllability is considered from the viewpoint of graph theory, and distance partition and almost equitable partition are introduced into switching topologies to quantitatively analyse the controllable state set of the system. For observability, sufficient and/or necessary conditions are presented in terms of the system matrices and the associated invariant subspace. Finally, some numerical simulations are worked out to illustrate the theoretical results.

Target controllability of multiagent systems under fixed and switching topologies

SummaryIn this article, the target controllability of multiagent systems under fixed and switching topologies is investigated, respectively. In the fixed topology setting, some necessary and/or sufficient algebraic and graph‐theoretic conditions are proposed, and the target controllable subspace is quantitatively studied by virtue of almost equitable graph vertex partitions. In the switching topology setting, based on the concepts of the invariant subspace and the target controllable state set, some necessary and sufficient algebraic conditions are obtained. Moreover, the target controllability is studied from the union graph perspective. The results show that when the union graph of all the possible topologies is target controllable, the multiagent system would be target controllable even if each of its subsystems is not. Numerical simulations are provided finally to verify the effectiveness of the theoretical results.

Did California Paid Family Leave Impact Infant Health?

The effects of paid parental leave policies on infant health have yet to be established. In this paper we investigate these effects by exploiting the introduction of California Paid Family Leave (PFL), the first program in the U.S. that specifically provides working parents with paid time off for bonding with a newborn. We measure health using the full census of infant hospitalizations in California and a set of control states, and implement a differences-in-differences approach. Our results suggest a decline in infant admissions, which is concentrated among those causes that are potentially affected by closer childcare (and to a lesser extent breastfeeding). Other admissions that are unlikely to be affected by parental leave do not exhibit the same pattern.

Controllability and observability of multi-agent systems with heterogeneous and switching topologies

ABSTRACTThis paper focuses on controllability and observability of multi-agent systems with heterogeneous and switching topologies, where the first- and the second-order information interaction topologies are different and switching. First, based on the controllable state set, a controllability criterion is obtained in terms of the controllability matrix corresponding to the switching sequence. Next, by virtue of the subspace sequence, two necessary and sufficient algebraic conditions are established for controllability in terms of the system matrices corresponding to all the possible topologies. Furthermore, controllability is considered from the graphic perspective. It is proved that the system is controllable if the union graph of all the possible topologies is controllable. With respect to observability, two sufficient and necessary conditions are derived by taking advantage of the system matrices and the corresponding invariant subspace, respectively. Finally, some simulation examples are worked out to illustrate the theoretical results.

Controllability and observability of switched multi-agent systems

ABSTRACTThis paper considers controllability and observability of switched multi-agent systems, which are composed of continuous-time and discrete-time subsystems. First, a controllability criterion is established in terms of the system matrices. Then, by virtue of the concepts of the invariant subspace and the controllable state set, a method is proposed to construct the switching sequence to ensure controllability of switched multi-agent systems, and a necessary and sufficient condition is obtained for controllability. Moreover, a necessary controllability condition is derived in terms of eigenvectors of the Laplican matrix. With respect to observability, two necessary and sufficient algebraic conditions are obtained. Finally, simulation examples are provided to illustrate the theoretical results.

Collapsible Pushdown Automata and Recursion Schemes

We consider recursion schemes (not assumed to be homogeneously typed , and hence not necessarily safe ) and use them as generators of (possibly infinite) ranked trees. A recursion scheme is essentially a finite typed deterministic term rewriting system that generates, when one applies the rewriting rules ad infinitum , an infinite tree, called its value tree . A fundamental question is to provide an equivalent description of the trees generated by recursion schemes by a class of machines. In this article, we answer this open question by introducing collapsible pushdown automata (CPDA), which are an extension of deterministic (higher-order) pushdown automata. A CPDA generates a tree as follows. One considers its transition graph, unfolds it, and contracts its silent transitions, which leads to an infinite tree, which is finally node labelled thanks to a map from the set of control states of the CPDA to a ranked alphabet. Our contribution is to prove that these two models, higher-order recursion schemes and collapsible pushdown automata, are equi-expressive for generating infinite ranked trees. This is achieved by giving effective transformations in both directions.

It is pointless to point in bounded heaps

In this paper we introduce a new symbolic semantics for a class of recursive programs which feature dynamic creation and unbounded allocation of objects. We use a symbolic representation of the program state in terms of equations to model the semantics of a program as a pushdown system with a finite set of control states and a finite stack alphabet. Our main technical result is a rigorous proof of the equivalence between the concrete and the symbolic semantics.Adding pointer fields gives rise to a Turing complete language. However, under the assumption that the number of reachable objects in the visible heap is bounded in all the computations of a program with pointers, we show how to construct a program without pointers that simulates it. Consequently, in the context of bounded visible heaps, programs with pointers are no more expressive than programs without them.We conclude by extending programs with a dynamic deallocation statement, an operation that affects all aliases of a deallocated object. We show how to extend the concrete and the symbolic semantics so to retain the previous equivalence result.

Pre-Medicated Murder: Violence and the Degree to Which the Mentally Ill Can Refuse Treatment

Objective: As part of the expansive overhaul of the mental health system, many states have passed laws that allow, under certain conditions, voluntary and involuntarily committed patients to refuse medication. While some predicted the consequences of these laws would be dire, the effect on violent behavior remains untested. This study measures the effect of various right to refuse medication laws on homicides.Method: Using a sample of the homicide rate of every US state between 1972 and 2001 (N=1,479), I compare the difference in homicide rates before and after a law change to that same difference in a set of control states to estimate the effect of laws aimed at extending the right to refuse medication to both voluntary and involuntarily committed mental health patients. Results: Laws designed to allow voluntarily committed patients to refuse medication are associated with a 0.8 increase in the homicide rate, and while point estimates suggest that allowing for review of requests to refuse medication are associated with a decrease in the homicide rate, the estimates are imprecise and statistically insignificant.Conclusion: Allowing voluntarily committed patients to refuse medication may entice some to enter in-patient facilities, but the brief and optional exposure to medication and their side effects may actually discourage treatment and increase violence.

Piecewise affine systems approach to control of biological networks

In terms of a piecewise affine system representation, which is a kind of hybrid system model, this article discusses a series of approaches to modelling, analysing and synthesizing a biological network such as a gene-regulatory network. First, the input assignment problem, the controllable state set problem (CSP) and the input trajectory generation problem are emphasized as control problems to be addressed for biological networks. Subsequently, after the modelling issue on biological networks developed in the systems and control community is briefly explained, the CSP is described in detail with reference to control of the quorum-sensing system in the pathogen Pseudomonas aeruginosa. Finally, an optimal control design method to the quorum-sensing system is proposed as a solution to the input trajectory generation problem.

On Controllability of Switched Linear Systems

This paper investigates the number of switchings and design of switching sequences for controllability of switched linear systems. Two related results are established. One is a new constructive approach to designing switching sequences. The controllable state set of each switching sequence designed via the approach coincides with the controllable subspace of switched linear systems. The other is a well-estimated value for the minimum number of switchings required for controllability. Each state in the controllable subspace can be steered to origin within this value of switching times.

Design of switching sequences for controllability realization of switched linear systems

In this paper, we study the problem of designing switching sequences for controllability of switched linear systems. Each controllable state set of designed switching sequences coincides with the controllable subspace. Both aperiodic and periodic switching sequences are considered. For the aperiodic case, a new approach is proposed to construct switching sequences, and the number of switchings involved in each designed switching sequence is shown to be upper bounded by d ( d - d 1 + 1 ) . Here d is the dimension of the controllable subspace, d 1 = dim ∑ i = 1 m 〈 A i | B i 〉 , where ( A i , B i ) are subsystems. For the periodic case, we show that the controllable subspace can be realized within d switching periods.

Reachability Analysis of Discrete-Time Systems With Disturbances

This paper presents new results that allow one to compute the set of states that can be robustly steered in a finite number of steps, via state feedback control, to a given target set. The assumptions that are made in this paper are that the system is discrete-time, nonlinear and time-invariant and subject to mixed constraints on the state and input. A persistent disturbance, dependent on the current state and input, acts on the system. Existing results are not able to address state- and input-dependent disturbances and the results in this paper are, therefore, a generalization of previously published results. One of the key aims of this paper is to present results such that one can perform the relevant set computations using polyhedral algebra and computational geometry software, provided the system is piecewise affine and the constraints are polygonal. Existing methods are only applicable to piecewise affine systems that either have no control inputs or no disturbances, whereas the results in this paper remove this limitation. Some simple examples are also given that show that, even if all the relevant sets are convex and the system is linear, convexity of the set of controllable states cannot be guaranteed.

Controllability and stabilizability of switched linear-systems

In this paper, we study the conjecture made in (IEEE Trans. Automat. Control 47 (8) (2002) 1401) concerning the existence of basic switching sequence for switched systems, and give it an affirmative answer and a construction method. This paper proves that for switched linear system, there exists a switching sequence such that the controllable state set of this switching sequence is equal to the controllable state set of the system. Hence, the controllability can be realized by using only one switching sequence. Then, the result is extended to the systems with time-delay in controls. Furthermore, we define the stabilizability of switched linear systems, and based on certain transformation of state coordinate, we give a necessary and sufficient condition for the stabilizability. Two examples are presented to illustrate the obtained results.

Algorithmic Analysis of Programs with Well Quasi-ordered Domains

Over the past few years increasing research effort has been directed towards the automatic verification of infinite-state systems. This paper is concerned with identifying general mathematical structures which can serve as sufficient conditions for achieving decidability. We present decidability results for a class of systems (called well-structured systems) which consist of a finite control part operating on an infinite data domain. The results assume that the data domain is equipped with a preorder which is a well quasi-ordering, such that the transition relation is “monotonic” (a simulation) with respect to the preorder. We show that the following properties are decidable for well-structured systems: • Reachability: whether a certain set of control states is reachable. Other safety properties can be reduced to the reachability problem. • Eventuality: whether all executions eventually reach a given set of control states (represented as AFp in CTL). • Simulation: whether there exists a simulation between a finite automaton and a well-structured system. The simulation problem will be shown to be decidable in both directions. We also describe how these general principles subsume several decidability results from the literature about timed automata, relational automata, Petri nets, and lossy channel systems.

Partitioned optical passive star (POPS) multiprocessor interconnection networks with distributed control

This paper presents a partitioned optical passive star (POPS) interconnection topology and a control methodology that, together, provide the high throughput and low latency required for tightly coupled multiprocessor interconnection applications. The POPS topology has constant and symmetric optical coupler fanout and only one coupler between any two nodes of the network. Distributed control is based on the state sequence routing paradigm which multiplexes the network between a small set of control states and defines control operations to be transformations of those states. These networks have highly scalable characteristics for optical power budget, resource count, and message latency. Optical power is uniformly distributed and the size of the system is not directly limited by the power budget. Resource complexity grows as O(n) for the couplers, O(n/spl radic/n) for transceivers, and O[/spl radic/nlog(n)] for control. We present analysis and simulation studies which demonstrate the ability of a POPS network to support large scale parallel processing (1024 nodes) using current device and coupler technology.

Formal verification of parallel programs

Two formal models for parallel computation are presented: an abstract conceptual model and a parallel-program model. The former model does not distinguish between control and data states. The latter model includes the capability for the representation of an infinite set of control states by allowing there to be arbitrarily many instruction pointers (or processes) executing the program. An induction principle is presented which treats the control and data state sets on the same ground. Through the use of “place variables,” it is observed that certain correctness conditions can be expressed without enumeration of the set of all possible control states. Examples are presented in which the induction principle is used to demonstrate proofs of mutual exclusion. It is shown that assertions-oriented proof methods are special cases of the induction principle. A special case of the assertions method, which is called parallel place assertions, is shown to be incomplete. A formalization of “deadlock” is then presented. The concept of a “norm” is introduced, which yields an extension, to the deadlock problem, of Floyd's technique for proving termination. Also discussed is an extension of the program model which allows each process to have its own local variables and permits shared global variables. Correctness of certain forms of implementation is also discussed. An Appendix is included which relates this work to previous work on the satisfiability of certain logical formulas.