Approximate Dynamic Programming for Constrained Piecewise Affine Systems with Stability and Safety Guarantees

Infinite-horizon optimal control of constrained piecewise affine (PWA) systems has been approximately addressed by hybrid model predictive control (MPC), which, however, has computational limitations, both in offline design and online implementation. In this paper, we consider an alternative approach based on approximate dynamic programming (ADP), an important class of methods in reinforcement learning. We accommodate non-convex union-of-polyhedra state constraints and linear input constraints into ADP by designing PWA penalty functions. PWA function approximation is used, which allows for a mixed-integer encoding to implement ADP. The main advantage of the proposed ADP method is its online computational efficiency. Particularly, we propose two control policies, which lead to solving a smaller-scale mixed-integer linear program than conventional hybrid MPC, or a single convex quadratic program, depending on whether the policy is implicitly determined online or explicitly computed offline. We characterize the stability and safety properties of the closed-loop systems, as well as the sub-optimality of the proposed policies, by quantifying the approximation errors of value functions and policies. We also develop an offline mixed-integer linear programming-based method to certify the reliability of the proposed method. Simulation results on an inverted pendulum with elastic walls and on an adaptive cruise control problem validate the control performance in terms of constraint satisfaction and CPU time

Cenozoic low temperature cooling history of the eastern Lhasa terrane: Implications for high-relief topography of external drainage area in the southern Tibetan Plateau

The Tibetan Plateau geographically contains internal and external drainage areas based on the distributions of river flows and catchments. The internal and external drainage areas display similar high-elevations, while their topographic reliefs are not comparable; the former shows a large low-relief surface, whereas the latter is characterized by relatively high relief. The eastern Lhasa terrane is a key tectonic component of the Tibetan Plateau. It is characterized by high topography and relief, but the thermal history of its basement remains relatively poorly constrained. In this study we report new apatite fission track data from the eastern part of the central Lhasa terrane to constrain the thermo-tectonic evolution of the external drainage area in the southern Tibetan Plateau. Twenty-one new AFT ages and associated thermal history models reveal that the basement underlying the external drainage area in southern Tibet experienced three main phases of rapid cooling in the Cenozoic. The Paleocene-early Eocene (∼60–48 Ma) cooling was likely induced by crustal shortening and associated rock exhumation, due to accelerated northward subduction of the NeoTethys oceanic lithosphere. A subsequent cooling pulse lasted from the late Eocene to early Oligocene (∼40–28 Ma), possibly due to the thickening and consequential erosion of the Lhasa lithosphere resulted from the continuous northward indentation of the India plate into Eurasia. The most recent rapid cooling event occurred in the middle Miocene-early Pliocene (∼16–4 Ma), likely induced by accelerated incision of the Lhasa River and local thrust faulting. Our AFT ages and published low-temperature thermochronological data reveal that the external drainage area experienced younger cooling events compared with the internal drainage area, and that the associated differentiated topographic evolution initiated at ca. 30 Ma. The contributing factors for the formation of the high-relief topography mainly contain active surface uplift, fault activity, and the enhanced incision of the Yarlung River

Late Oligocene - Miocene morpho-tectonic evolution of the central Gangdese batholith constrained by low-temperature thermochronology

The morpho-tectonic evolution of the Tibetan Plateau is controlled by complicated interactions between tectonic uplift and surface erosion. The Gangdese batholith in the southern Lhasa terrane is a key orogenic belt for exploring the complicated morpho-tectonic evolution of the Tibetan Plateau. In this contribution, we apply apatite fission track (AFT) thermochronology to constrain the thermo-tectonic evolution of the central segment of the Gangdese batholith. Twenty-four granitoid samples were collected from both river valleys (e.g., the Yarlung and Xiang Rivers) and from the internal batholith areas located farther from river drainage (and/or local faults) networks. All samples exhibit Miocene AFT ages between ∼19.9 and ∼ 6.1 Ma. Inverse thermal history modeling results reveal that the central Gangdese batholith underwent a two-stage accelerated basement cooling in the Miocene. The first cooling stage took place during the late Oligocene to middle Miocene (∼25–15 Ma), this period of moderate to rapid basement cooling coincides with activity along the Gangdese thrust and Great Counter thrust system, and the Oligocene-Miocene delamination of the Lhasa lithosphere and concomitant asthenosphere upwelling. These tectonic processes acted as first-order control on regional basement uplift, denudation and exhumation. Second, a middle-late Miocene (∼14–5 Ma) rapid cooling is widely recognized in the whole Gangdese batholith. We suggest that this middle-late Miocene cooling is due to exhumation in response to tectonic and surface erosion processes such as N-S normal faults and enhanced river incision induced by the intensification of Asian monsoon. Finally, in combination with published low-temperature thermochronological and paleoaltimetry data, it is deduced that the present-day low-relief landscape of the southern Lhasa terrane resulted from a long-term balance between intense regional tectonic activity and surface erosion.24 month embargo; available online: 5 September 2022This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Structural setting of the Narusongduo Pb-Zn ore deposit in the Gangdese belt, central Tibet

The Narusongduo Pb-Zn deposit is located at the northern boundary of the Luobadui-Milashan fault zone (LMF) in central Tibet and is spatially associated with the Linzizong volcanic succession (LVS). Our study indicates that the regional structural setting was formed by two-stage tectonic events. The first stage, spanning from the late Mesozoic to early Paleocene, is characterized by significant N-S crustal shortening associated with the Cordilleran-type orogeny along the Gangdese arc. The region's Paleozoic-Mesozoic metasedimentary rocks were penetratively strained. Locally deformation was largely partitioned along the LMF. During the second stage (ca. 66-55 Ma), the area was affected by extensive multi-stage Linzizong volcanism, including caldera formation, as well as a coaxial N-S propagative deformation with a distinctive lower shortening rate. We recognized two types of mineralization, both were formed during the second stage. The first type of mineralization (orebody III) is governed by fractures within the extensively deformed Paleozoic carbonate rocks at the LMF's footwall. The overlying LVS, however, includes discrete but numerous mineralized sections. The terminal splays of the ore shoots typify the products of hydraulic fracturing. We propose that the propagative compressive deformation drained fluid reservoirs at depth to higher levels via the "Fault valve" effect. Episodic fluid influxes and mineral deposition formed the time-integrated mineralization. The second type of mineralization (orebody I) is hosted in the LVS in a number of breccia pipes and dykes that were controlled by the structural weaknesses generated by the intersection of the radial and ring fractures. Mineralization occurs as veinlets in the matrix and clasts inside the breccias, which are characterized by multi-stage brittle cracking, fluid injection and mineral precipitation. It is interpreted that the multi-stage magmatism (ca. 66-55 Ma) triggered repeated hydrothermal activities and incremental mineralization within the ore-bearing breccia bodies